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Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",69,536870920]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",69,536870920]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u6535b15c-8b04-4fb6-a3a7-16bbd9c3b689logseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",48,536870920]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",90,536870920]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[54,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[54,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",38,536870920]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u6535b15c-8139-4526-8096-acaf816dc1f4logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",75,536870920]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",75,536870920]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",32,536870920]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u6535b15c-c7c9-4b3d-9561-89b1feef9439logseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",63,536870920]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",63,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",46,536870920]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6535b15c-b747-4a0d-8658-bae45eb49967logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0 logseq____&logseq____& \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&=-p logseq____&logseq____& x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",71,536870920]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",105,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",42,536870920]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u6535b15c-439e-494c-9221-1f56fdcc06d0logseq____",536870920]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870920]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",72,536870920]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[58,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[58,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",28,536870920]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u6535b15c-c9f4-4511-ac22-929ead0e5a1flogseq____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",61,536870920]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u6535b15c-34c4-4728-b78b-a7eee3bd9b1blogseq____",536870920]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&= p logseq____&, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&=0\\\\\\\\\\nx^2-7x+12logseq____&=0\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",100,536870920]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",100,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6535b15c-f27d-4875-9df2-bc12828a46e0logseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",76,536870920]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u6535b15c-8d6c-4f3a-b813-ff01ff6f7178logseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",97,536870920]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",77,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",31,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u6535b15c-1fa7-4e3d-abc7-ddfe4fc10a7blogseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",59,536870920]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",46,536870920]],[logseq____"^15logseq____",[63,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[63,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",40,536870920]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",46,536870920]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6535b15c-1771-40c9-a1a8-d4c99dc75f2dlogseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&, a,b,logseq____>0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",102,536870920]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",102,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",46,536870920]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u6535b15c-b4f4-44f4-b450-da3f2cdb3098logseq____",536870920]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",53,536870920]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",69,536870920]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6535b15c-4346-4653-9058-7f278ef503bblogseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",83,536870920]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",61,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[66,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u6535b15c-501b-4ce0-beaa-5e67ed8dd56dlogseq____",536870920]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870920]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",93,536870920]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",79,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",33,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[67,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[67,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",33,536870920]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u6535b15c-359c-43d8-b4d1-5869c7512a95logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",95,536870920]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",95,536870920]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u6535b15c-d8a3-4c5d-83b3-109f9f48d1a9logseq____",536870920]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870920]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",95,536870920]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[69,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[69,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[69,logseq____"^Hlogseq____",35,536870920]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u6535b15c-820c-4d0a-ae3c-7694e3777fa3logseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Qlogseq____",logseq____"https://www.wolframalpha.comlogseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",103,536870920]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",103,536870920]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",45,536870920]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",47,536870920]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u6535b15c-e37e-4427-9328-8a5c8d953e53logseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",105,536870920]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",105,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",27,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[71,logseq____"^Hlogseq____",27,536870920]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u6535b15c-b570-4aaf-8ce3-bf57b68ac877logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",41,536870920]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",45,536870920]],[logseq____"^15logseq____",[72,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[72,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[72,logseq____"^Hlogseq____",45,536870920]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",false,536870920]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u6535b15c-9bb3-49f6-b97a-3aac6932a595logseq____",536870920]],[logseq____"^15logseq____",[73,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",68,536870920]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",95,536870920]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u6535b15c-212e-43e1-b083-33e0ef19d8c4logseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",73,536870920]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",73,536870920]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u6535b15c-ffa1-444d-a635-7e2534a0e72blogseq____",536870920]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870920]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",58,536870920]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",32,536870920]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[75,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[75,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",32,536870920]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u6535b15c-00b6-4ed6-9cc1-f317668b93fblogseq____",536870920]],[logseq____"^15logseq____",[76,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",50,536870920]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u6535b15c-a4de-4e57-879f-9ab757119d3alogseq____",536870920]],[logseq____"^15logseq____",[77,logseq____"^Qlogseq____",logseq____"# [[Wurzelgleichung]]logseq____",536870920]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",78,536870920]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",90,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",31,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[77,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[77,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[77,logseq____"^Hlogseq____",31,536870920]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u6535b15c-384d-4ad3-bdf3-3ff2357d2b99logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",54,536870920]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",90,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[78,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[78,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[78,logseq____"^Hlogseq____",30,536870920]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u6535b15c-6178-4d7a-b40d-921c89b5b032logseq____",536870920]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870920]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",65,536870920]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",69,536870920]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[79,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[79,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[79,logseq____"^Hlogseq____",29,536870920]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u6535b15c-2019-4b44-b805-899858a140e6logseq____",536870920]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nax^2+bx+clogseq____&=0logseq____&|:a\\\\quadlogseq____&a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&= 0\\\\\\\\\\nplogseq____&=\\\\frac ba,logseq____&q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&=0\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",78,536870920]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",78,536870920]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u6535b15c-2c0c-4dd5-b507-fd7244089356logseq____",536870920]],[logseq____"^15logseq____",[81,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870920]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",94,536870920]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",93,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[81,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[81,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u6535b15c-075b-4c78-8d15-cd9e8b338bf3logseq____",536870920]],[logseq____"^15logseq____",[82,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870920]],[logseq____"^15logseq____",[82,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[82,logseq____"^Flogseq____",88,536870920]],[logseq____"^15logseq____",[82,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[82,logseq____"^Vlogseq____",88,536870920]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[82,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u6535b15c-d948-4f99-9460-9f1d2104530clogseq____",536870920]],[logseq____"^15logseq____",[83,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{y^2}=\\\\left|y\\\\right|\\\\\\\\\\n\\\\sqrt[5]{a\\\\sqrt[3]a}=\\\\sqrt[5]{\\\\sqrt[3]{a^3}\\\\sqrt[3]a}\\nlogseq____&=\\\\sqrt[5]{\\\\sqrt[3]{a^4}}\\n=\\\\sqrt[5]{a^\\\\frac43}\\n=a^{\\\\frac43\\\\frac15}=a^\\\\frac4{15}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",61,536870920]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",61,536870920]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u6535b15c-167e-45e5-8f4b-9ac0c9c6cfcblogseq____",536870920]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",58,536870920]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",58,536870920]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",34,536870920]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",34,536870920]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u6535b15c-8779-4878-90bc-5b6f9dd09840logseq____",536870920]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",96,536870920]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",49,536870920]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u6535b15c-1ca1-4c47-b928-152fdad246e2logseq____",536870920]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870920]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",67,536870920]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",67,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",33,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",39,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[86,logseq____"^Hlogseq____",39,536870920]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u6535b15c-e5fc-4a44-949f-d133fb3a12adlogseq____",536870920]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",101,536870920]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",101,536870920]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u6535b15c-8232-430a-8712-1b143c5d1fd7logseq____",536870920]],[logseq____"^15logseq____",[88,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",99,536870920]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",48,536870920]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u6535b15c-b147-446a-8215-a055bd044eaalogseq____",536870920]],[logseq____"^15logseq____",[89,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c} (a+b)^0logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 \\\\\\\\\\n(a+b)^1logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^2logseq____&logseq____&logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 2 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^3logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 3 logseq____&logseq____& 3 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^4logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 4 logseq____&logseq____& 6 logseq____&logseq____& 4 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^5logseq____&logseq____&logseq____& 1 logseq____&logseq____& 5 logseq____&logseq____& 10 logseq____&logseq____& 10 logseq____&logseq____& 5 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^6logseq____&logseq____& 1 logseq____&logseq____& 6 logseq____&logseq____& 15 logseq____&logseq____& 20 logseq____&logseq____& 15 logseq____&logseq____& 6 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^7logseq____&1 logseq____&logseq____& 7 logseq____&logseq____&21 logseq____&logseq____& 35 logseq____&logseq____& 35 logseq____&logseq____& \\\\cdots\\\\end{array}logseq____",536870920]],[logseq____"^15logseq____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",79,536870920]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",79,536870920]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u6535b15c-a909-4bf4-be0d-04ad8283feaclogseq____",536870920]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870920]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",69,536870920]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[90,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[90,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[90,logseq____"^Hlogseq____",28,536870920]],[logseq____"^15logseq____",[90,logseq____"^Hlogseq____",38,536870920]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u6535b15c-74b6-45f3-8519-a3234ccf447dlogseq____",536870920]],[logseq____"^15logseq____",[91,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\na^nlogseq____&=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____& a,blogseq____>0\\\\\\\\\\na^2b^2logseq____&=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&=a^{nm}\\\\\\\\\\na^0logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",48,536870920]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",48,536870920]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u6535b15c-2219-4d77-9609-5b40657c89aflogseq____",536870920]],[logseq____"^15logseq____",[92,logseq____"^Qlogseq____",logseq____"logseq____",536870920]],[logseq____"^15logseq____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",84,536870920]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",58,536870920]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u6535b15c-f32c-4d3f-a9ad-21ceeda0ef76logseq____",536870920]],[logseq____"^15logseq____",[93,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870920]],[logseq____"^15logseq____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",89,536870920]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",79,536870920]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[93,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u6535b15c-78a2-4c27-9ec3-067f025b0787logseq____",536870920]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(2x+y)^4logseq____&=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5logseq____&=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",93,536870920]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",93,536870920]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u6535b15c-0300-4d97-8071-69091445b108logseq____",536870920]],[logseq____"^15logseq____",[95,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870920]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",101,536870920]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[95,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[95,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[95,logseq____"^Hlogseq____",37,536870920]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u6535b15c-d04e-4be9-8756-30def9f2b405logseq____",536870920]],[logseq____"^15logseq____",[96,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[96,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[96,logseq____"^Flogseq____",49,536870920]],[logseq____"^15logseq____",[96,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[96,logseq____"^Vlogseq____",49,536870920]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[96,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[96,logseq____"^;logseq____",logseq____"~u6535b15c-a11c-4214-8c04-c184c3a23abflogseq____",536870920]],[logseq____"^15logseq____",[97,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{a+5}-\\\\sqrt{x+3}logseq____&=2\\\\sqrt(x+1) logseq____&|logseq____&()^2\\\\\\\\\\n\\\\left(\\\\sqrt{x+5}-\\\\sqrt{x+3}\\\\right)^2logseq____&=4(x+1)\\\\\\\\\\n(x+5)-2\\\\sqrt{x+5}\\\\sqrt{x+3}+(x+3)logseq____&=4x+4logseq____&|logseq____&-(2x+8)\\\\\\\\\\n-2\\\\sqrt{(x+5)(x+3)}logseq____&=2x-4 logseq____&|logseq____&()^2\\\\\\\\\\n4(x+5)(x+3)logseq____&=4x^2-16x+16\\\\\\\\\\n4x^2+32x+60logseq____&=4x^2-16x+16logseq____&|logseq____&-4x^2+16x-16\\\\\\\\\\n48x+44logseq____&=0\\\\quad 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2}\\\\quad -5\\\\le xlogseq____<3$\\n\\\\begin{align}\\nx+5logseq____&\\\\le0\\\\\\\\\\n|x+5|logseq____&=x+5\\\\\\\\\\nx-3logseq____&logseq____<0\\\\\\\\\\n|x-3|logseq____&=-(x-3)=-x+3\\\\\\\\\\nx+5logseq____&logseq____<2(-x+3)\\\\\\\\\\nx+5logseq____&logseq____<-2x+6 logseq____&|logseq____&+2x\\\\\\\\\\n3xlogseq____&logseq____<1 logseq____&|logseq____& :3\\\\\\\\\\nxlogseq____&logseq____<\\\\frac13\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-5\\\\le 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[[Lösungsmengen]]logseq____",536870921]],[logseq____"^15logseq____",[155,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[155,logseq____"^Flogseq____",177,536870921]],[logseq____"^15logseq____",[155,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[155,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[155,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[155,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[155,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[155,logseq____"^?logseq____",[logseq____"^ 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*(-1)\\\\\\\\\\nxlogseq____&logseq____>11\\n\\\\end{align}\\n\\\\begin{align}\\nL_3=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____>3,xlogseq____>11\\\\right\\\\}=(11,\\\\infty)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[156,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[156,logseq____"^Flogseq____",154,536870921]],[logseq____"^15logseq____",[156,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[156,logseq____"^Vlogseq____",149,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[156,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[156,logseq____"^;logseq____",logseq____"~u6535b15c-1bf9-42d2-8355-5b61bf9eddbdlogseq____",536870921]],[logseq____"^15logseq____",[157,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870921]],[logseq____"^15logseq____",[157,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[157,logseq____"^Flogseq____",151,536870921]],[logseq____"^15logseq____",[157,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[157,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[157,logseq____"^Hlogseq____",36,536870921]],[logseq____"^15logseq____",[157,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[157,logseq____"^;logseq____",logseq____"~u6535b15c-6858-49cd-af0c-1695a646820clogseq____",536870921]],[logseq____"^15logseq____",[158,logseq____"^Qlogseq____",logseq____"Bei Multiplikation oder Division mit einem Betrag einer negativen Zahl nicht Anwendbar, da ein [[Betrag]] immer Positiv 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von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]]) die den gleichen [[Abstand]] r ([[Radius]]) zu einem [festen Punkt]([[Fester Punkt]]) ([[Mittelpunkt]])logseq____",536870921]],[logseq____"^15logseq____",[159,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[159,logseq____"^Flogseq____",166,536870921]],[logseq____"^15logseq____",[159,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[159,logseq____"^Vlogseq____",166,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",108,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",109,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",118,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",125,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",126,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",108,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",109,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",112,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",118,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",125,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",126,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",127,536870921]],[logseq____"^15logseq____",[159,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[159,logseq____"^;logseq____",logseq____"~u6535b15c-aa5c-48e0-af38-8c35d17a461dlogseq____",536870921]],[logseq____"^15logseq____",[160,logseq____"^Qlogseq____",logseq____"wie [[Ellipse]] nur statt [[Summe]] [[Differenz]]logseq____",536870921]],[logseq____"^15logseq____",[160,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[160,logseq____"^Flogseq____",178,536870921]],[logseq____"^15logseq____",[160,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[160,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",120,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",123,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[160,logseq____"^Hlogseq____",111,536870921]],[logseq____"^15logseq____",[160,logseq____"^Hlogseq____",120,536870921]],[logseq____"^15logseq____",[160,logseq____"^Hlogseq____",123,536870921]],[logseq____"^15logseq____",[160,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[160,logseq____"^;logseq____",logseq____"~u6535b15c-efff-4881-a8d3-a9cfccc59813logseq____",536870921]],[logseq____"^15logseq____",[161,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup 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[[Mengen]]logseq____",536870921]],[logseq____"^15logseq____",[162,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[162,logseq____"^Flogseq____",122,536870921]],[logseq____"^15logseq____",[162,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[162,logseq____"^Vlogseq____",122,536870921]],[logseq____"^15logseq____",[162,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[162,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[162,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870921]],[logseq____"^15logseq____",[162,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[162,logseq____"^Hlogseq____",127,536870921]],[logseq____"^15logseq____",[162,logseq____"^17logseq____",false,536870921]],[logseq____"^15logseq____",[162,logseq____"^;logseq____",logseq____"~u6535b15c-b252-477d-ab08-6b8d8a7b03e7logseq____",536870921]],[logseq____"^15logseq____",[163,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1b}\\\\quad xlogseq____<-2\\\\quad\\\\text{Wiederspricht Bedingung}\\\\quad x\\\\ge3$logseq____",536870921]],[logseq____"^15logseq____",[163,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[163,logseq____"^Flogseq____",130,536870921]],[logseq____"^15logseq____",[163,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[163,logseq____"^Vlogseq____",172,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[163,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[163,logseq____"^;logseq____",logseq____"~u6535b15c-19ff-4d74-98dc-7ae83f4703a7logseq____",536870921]],[logseq____"^15logseq____",[164,logseq____"^Qlogseq____",logseq____"[Menge]([[Mengen]]) an [Punkten]([[Punkte]]) $(x,y)$ der [Ebene]([[Ebenen]]) bei denen die [[Summe]] der [Abstände]([[Abstand]]) der Punkte zu zwei [festen Punkten]([[Fester Punkt]]) $F_1,F_2$ ([Brennpunkte]([[Brennpunkt]])) [[konstant]] istlogseq____",536870921]],[logseq____"^15logseq____",[164,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[164,logseq____"^Flogseq____",136,536870921]],[logseq____"^15logseq____",[164,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[164,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",108,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",113,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",115,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",118,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",120,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",125,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",126,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",108,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",113,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",115,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",118,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",120,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",125,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",126,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",127,536870921]],[logseq____"^15logseq____",[164,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[164,logseq____"^;logseq____",logseq____"~u6535b15c-0f4d-4aca-a0c0-b2f83851b4e0logseq____",536870921]],[logseq____"^15logseq____",[165,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nM=\\\\left\\\\{\\\\underbrace{(x,y)}_\\\\text{Punkte 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Ebene}\\\\in\\\\Reals^2\\\\middle|y=|x|\\\\right\\\\}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[165,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[165,logseq____"^Flogseq____",179,536870921]],[logseq____"^15logseq____",[165,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[165,logseq____"^Vlogseq____",179,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[165,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[165,logseq____"^;logseq____",logseq____"~u6535b15c-cec1-429a-86e6-2ed575dbfbbclogseq____",536870921]],[logseq____"^15logseq____",[166,logseq____"^Qlogseq____",logseq____"## [[Kreis]]logseq____",536870921]],[logseq____"^15logseq____",[166,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[166,logseq____"^Flogseq____",170,536870921]],[logseq____"^15logseq____",[166,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[166,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[166,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870921]],[logseq____"^15logseq____",[166,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[166,logseq____"^Hlogseq____",107,536870921]],[logseq____"^15logseq____",[166,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[166,logseq____"^;logseq____",logseq____"~u6535b15c-a666-497e-a27b-a5eb5dae6648logseq____",536870921]],[logseq____"^15logseq____",[167,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup 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[[Betrag]]logseq____",536870921]],[logseq____"^15logseq____",[170,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[170,logseq____"^Flogseq____",148,536870921]],[logseq____"^15logseq____",[170,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[170,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[170,logseq____"^?logseq____",[logseq____"^ 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$\\\\infty$\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____>4\\\\right\\\\}=:(4,\\\\infty)\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[173,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[173,logseq____"^Flogseq____",182,536870921]],[logseq____"^15logseq____",[173,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[173,logseq____"^Vlogseq____",148,536870921]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[173,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[173,logseq____"^;logseq____",logseq____"~u6535b15c-ed59-4be8-a8bb-5180a8edaee4logseq____",536870921]],[logseq____"^15logseq____",[174,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[174,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[174,logseq____"^Flogseq____",164,536870921]],[logseq____"^15logseq____",[174,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[174,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[174,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[174,logseq____"^;logseq____",logseq____"~u6535b15c-041c-4864-8360-61f331baf366logseq____",536870921]],[logseq____"^15logseq____",[175,logseq____"^Qlogseq____",logseq____"\\\\begin{gather}\\n\\\\frac{|x+5|}{|x-3|}logseq____<2\\\\quad\\\\Bigm|*|x-3|\\\\qquad 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Lösung mit [[Fallunterscheidung]]logseq____",536870921]],[logseq____"^15logseq____",[176,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[176,logseq____"^Flogseq____",147,536870921]],[logseq____"^15logseq____",[176,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[176,logseq____"^Vlogseq____",147,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[176,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[176,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[176,logseq____"^Hlogseq____",110,536870921]],[logseq____"^15logseq____",[176,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[176,logseq____"^;logseq____",logseq____"~u6535b15c-7785-4e86-b170-daf0b934c72flogseq____",536870921]],[logseq____"^15logseq____",[177,logseq____"^Qlogseq____",logseq____"$\\\\{a,b,c\\\\}$logseq____",536870921]],[logseq____"^15logseq____",[177,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[177,logseq____"^Flogseq____",162,536870921]],[logseq____"^15logseq____",[177,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[177,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[177,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[177,logseq____"^;logseq____",logseq____"~u6535b15c-7326-4b18-b8cc-2157f6db20a7logseq____",536870921]],[logseq____"^15logseq____",[178,logseq____"^Qlogseq____",logseq____"## [[Hyperbel]]logseq____",536870921]],[logseq____"^15logseq____",[178,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[178,logseq____"^Flogseq____",136,536870921]],[logseq____"^15logseq____",[178,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[178,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[178,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870921]],[logseq____"^15logseq____",[178,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[178,logseq____"^Hlogseq____",119,536870921]],[logseq____"^15logseq____",[178,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[178,logseq____"^;logseq____",logseq____"~u6535b15c-3150-470b-b052-b4671d8d811blogseq____",536870921]],[logseq____"^15logseq____",[179,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[179,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[179,logseq____"^Flogseq____",138,536870921]],[logseq____"^15logseq____",[179,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[179,logseq____"^Vlogseq____",137,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[179,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[179,logseq____"^;logseq____",logseq____"~u6535b15c-bf8f-426b-834a-e60872a0a220logseq____",536870921]],[logseq____"^15logseq____",[180,logseq____"^Qlogseq____",logseq____"$$L=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_{0\\\\notin 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1} \\\\quad xlogseq____<-5$\\n\\\\begin{align}\\nx+5logseq____&logseq____<0\\\\\\\\\\n|x+5|logseq____&=-(x+5)=-x-5\\\\\\\\\\nx-3logseq____&logseq____<0\\\\\\\\\\n|x-3|logseq____&=-(x-3)=-x+3\\\\\\\\\\n-x-5logseq____&logseq____< 2(-x+3)\\\\\\\\\\n-x-5logseq____&logseq____<-2x+6 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Aussagenlogseq____",536870923]],[logseq____"^15logseq____",[207,logseq____"^Blogseq____",1698017628871,536870923]],[logseq____"^15logseq____",[207,logseq____"^;logseq____",logseq____"~u6535b15c-8756-449b-9d15-a4fcdd40e76alogseq____",536870923]],[logseq____"^15logseq____",[208,logseq____"^Klogseq____",1698017628885,536870923]],[logseq____"^15logseq____",[208,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[208,logseq____"^Ylogseq____",logseq____"schreibweiselogseq____",536870923]],[logseq____"^15logseq____",[208,logseq____"^11logseq____",logseq____"Schreibweiselogseq____",536870923]],[logseq____"^15logseq____",[208,logseq____"^Blogseq____",1698017628885,536870923]],[logseq____"^15logseq____",[208,logseq____"^;logseq____",logseq____"~u6535b15c-4882-4d69-9bfc-4bed89d57791logseq____",536870923]],[logseq____"^15logseq____",[209,logseq____"^Klogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[209,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[209,logseq____"^Ylogseq____",logseq____"belegunglogseq____",536870923]],[logseq____"^15logseq____",[209,logseq____"^11logseq____",logseq____"Belegunglogseq____",536870923]],[logseq____"^15logseq____",[209,logseq____"^Blogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[209,logseq____"^;logseq____",logseq____"~u6535b15c-7146-4a61-b02f-a58ffdd08b8elogseq____",536870923]],[logseq____"^15logseq____",[210,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870923]],[logseq____"^15logseq____",[210,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[210,logseq____"^Flogseq____",214,536870923]],[logseq____"^15logseq____",[210,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[210,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",191,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",201,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",208,536870923]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",191,536870923]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",201,536870923]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",208,536870923]],[logseq____"^15logseq____",[210,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[210,logseq____"^;logseq____",logseq____"~u6535b15c-dd23-4fc8-b886-37cf02c94fa9logseq____",536870923]],[logseq____"^15logseq____",[211,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870923]],[logseq____"^15logseq____",[211,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[211,logseq____"^Flogseq____",210,536870923]],[logseq____"^15logseq____",[211,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[211,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",197,536870923]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[211,logseq____"^Hlogseq____",197,536870923]],[logseq____"^15logseq____",[211,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[211,logseq____"^;logseq____",logseq____"~u6535b15c-96a7-48b7-9900-3cb16d89107alogseq____",536870923]],[logseq____"^15logseq____",[212,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870923]],[logseq____"^15logseq____",[212,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[212,logseq____"^Flogseq____",217,536870923]],[logseq____"^15logseq____",[212,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[212,logseq____"^Vlogseq____",213,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",191,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[212,logseq____"^Hlogseq____",191,536870923]],[logseq____"^15logseq____",[212,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[212,logseq____"^;logseq____",logseq____"~u6535b15c-ffb5-4ab2-9211-74d7ee54c445logseq____",536870923]],[logseq____"^15logseq____",[213,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870923]],[logseq____"^15logseq____",[213,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[213,logseq____"^Flogseq____",216,536870923]],[logseq____"^15logseq____",[213,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[213,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",191,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[213,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[213,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",191,536870923]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",205,536870923]],[logseq____"^15logseq____",[213,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[213,logseq____"^;logseq____",logseq____"~u6535b15c-c1a5-4eca-b8e4-14fb7862b8a9logseq____",536870923]],[logseq____"^15logseq____",[214,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870923]],[logseq____"^15logseq____",[214,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[214,logseq____"^Flogseq____",223,536870923]],[logseq____"^15logseq____",[214,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[214,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",198,536870923]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[214,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[214,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[214,logseq____"^Hlogseq____",198,536870923]],[logseq____"^15logseq____",[214,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[214,logseq____"^;logseq____",logseq____"~u6535b15c-cf18-41bd-b8d8-4d6417d59627logseq____",536870923]],[logseq____"^15logseq____",[215,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[215,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[215,logseq____"^Flogseq____",235,536870923]],[logseq____"^15logseq____",[215,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[215,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",36,536870923]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[215,logseq____"^Hlogseq____",36,536870923]],[logseq____"^15logseq____",[215,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[215,logseq____"^;logseq____",logseq____"~u6535b15c-1c62-4ca6-82b0-4a30a697f598logseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der [[Variablen]])logseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Flogseq____",220,536870923]],[logseq____"^15logseq____",[216,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[216,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",199,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",209,536870923]],[logseq____"^15logseq____",[216,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[216,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[216,logseq____"^Hlogseq____",199,536870923]],[logseq____"^15logseq____",[216,logseq____"^Hlogseq____",209,536870923]],[logseq____"^15logseq____",[216,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[216,logseq____"^;logseq____",logseq____"~u6535b15c-f4f1-45ea-94a4-de2dc2575b03logseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Flogseq____",213,536870923]],[logseq____"^15logseq____",[217,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[217,logseq____"^Vlogseq____",213,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",191,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",194,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",195,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",202,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",209,536870923]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",194,536870923]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",195,536870923]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",202,536870923]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",209,536870923]],[logseq____"^15logseq____",[217,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[217,logseq____"^;logseq____",logseq____"~u6535b15c-bdaa-4dd1-87b5-79b03e956b7flogseq____",536870923]],[logseq____"^15logseq____",[218,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870923]],[logseq____"^15logseq____",[218,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[218,logseq____"^Flogseq____",231,536870923]],[logseq____"^15logseq____",[218,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[218,logseq____"^Vlogseq____",229,536870923]],[logseq____"^15logseq____",[218,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[218,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[218,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[218,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870923]],[logseq____"^15logseq____",[218,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[218,logseq____"^Hlogseq____",207,536870923]],[logseq____"^15logseq____",[218,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[218,logseq____"^;logseq____",logseq____"~u6535b15c-785e-4423-9aff-d4a8955d1548logseq____",536870923]],[logseq____"^15logseq____",[219,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870923]],[logseq____"^15logseq____",[219,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[219,logseq____"^Flogseq____",223,536870923]],[logseq____"^15logseq____",[219,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[219,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ulogseq____",197,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[219,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[219,logseq____"^;logseq____",logseq____"~u6535b15c-3666-4f5f-8172-74318ff04615logseq____",536870923]],[logseq____"^15logseq____",[220,logseq____"^Qlogseq____",logseq____"### [[Aussageformel]]logseq____",536870923]],[logseq____"^15logseq____",[220,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[220,logseq____"^Flogseq____",228,536870923]],[logseq____"^15logseq____",[220,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[220,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[220,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[220,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[220,logseq____"^Hlogseq____",205,536870923]],[logseq____"^15logseq____",[220,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[220,logseq____"^;logseq____",logseq____"~u6535b15c-5390-4e0a-b30b-46a51516f485logseq____",536870923]],[logseq____"^15logseq____",[221,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870923]],[logseq____"^15logseq____",[221,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[221,logseq____"^Flogseq____",237,536870923]],[logseq____"^15logseq____",[221,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[221,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[221,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[221,logseq____"^Ulogseq____",196,536870923]],[logseq____"^15logseq____",[221,logseq____"^Hlogseq____",196,536870923]],[logseq____"^15logseq____",[221,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[221,logseq____"^;logseq____",logseq____"~u6535b15c-2802-4093-8b3e-df42ed2aa20alogseq____",536870923]],[logseq____"^15logseq____",[222,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870923]],[logseq____"^15logseq____",[222,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[222,logseq____"^Flogseq____",214,536870923]],[logseq____"^15logseq____",[222,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[222,logseq____"^Vlogseq____",214,536870923]],[logseq____"^15logseq____",[222,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[222,logseq____"^Ulogseq____",198,536870923]],[logseq____"^15logseq____",[222,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[222,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[222,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[222,logseq____"^;logseq____",logseq____"~u6535b15c-dc88-4afb-b08f-dc4015c2328blogseq____",536870923]],[logseq____"^15logseq____",[223,logseq____"^Qlogseq____",logseq____"### [[Tantologie]]logseq____",536870923]],[logseq____"^15logseq____",[223,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[223,logseq____"^Flogseq____",213,536870923]],[logseq____"^15logseq____",[223,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[223,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[223,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[223,logseq____"^Ulogseq____",197,536870923]],[logseq____"^15logseq____",[223,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[223,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[223,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[223,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[223,logseq____"^Hlogseq____",197,536870923]],[logseq____"^15logseq____",[223,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[223,logseq____"^;logseq____",logseq____"~u6535b15c-2cc3-4f14-b068-45847b6d0673logseq____",536870923]],[logseq____"^15logseq____",[224,logseq____"^Qlogseq____",logseq____"Weitere [[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[224,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[224,logseq____"^Flogseq____",211,536870923]],[logseq____"^15logseq____",[224,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[224,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[224,logseq____"^Ulogseq____",36,536870923]],[logseq____"^15logseq____",[224,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[224,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[224,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[224,logseq____"^Hlogseq____",36,536870923]],[logseq____"^15logseq____",[224,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[224,logseq____"^;logseq____",logseq____"~u6535b15c-8d3b-4aac-9ee8-823c2e0f141elogseq____",536870923]],[logseq____"^15logseq____",[225,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870923]],[logseq____"^15logseq____",[225,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[225,logseq____"^Flogseq____",221,536870923]],[logseq____"^15logseq____",[225,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[225,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[225,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[225,logseq____"^Ulogseq____",193,536870923]],[logseq____"^15logseq____",[225,logseq____"^Hlogseq____",193,536870923]],[logseq____"^15logseq____",[225,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[225,logseq____"^;logseq____",logseq____"~u6535b15c-2355-4bdd-ab71-2d7e5e3d22b1logseq____",536870923]],[logseq____"^15logseq____",[226,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870923]],[logseq____"^15logseq____",[226,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[226,logseq____"^Flogseq____",220,536870923]],[logseq____"^15logseq____",[226,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[226,logseq____"^Vlogseq____",220,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",43,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",204,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[226,logseq____"^Hlogseq____",43,536870923]],[logseq____"^15logseq____",[226,logseq____"^Hlogseq____",204,536870923]],[logseq____"^15logseq____",[226,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[226,logseq____"^;logseq____",logseq____"~u6535b15c-9aee-437d-8179-6bf642cc5552logseq____",536870923]],[logseq____"^15logseq____",[227,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[227,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[227,logseq____"^Flogseq____",215,536870923]],[logseq____"^15logseq____",[227,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[227,logseq____"^Vlogseq____",215,536870923]],[logseq____"^15logseq____",[227,logseq____"^Ulogseq____",36,536870923]],[logseq____"^15logseq____",[227,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[227,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[227,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[227,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[227,logseq____"^;logseq____",logseq____"~u6535b15c-cdca-4be2-b8a9-d0301180acdalogseq____",536870923]],[logseq____"^15logseq____",[228,logseq____"^Qlogseq____",logseq____"### [[Aussagenlogische Variable]]logseq____",536870923]],[logseq____"^15logseq____",[228,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[228,logseq____"^Flogseq____",232,536870923]],[logseq____"^15logseq____",[228,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[228,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[228,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[228,logseq____"^Ulogseq____",192,536870923]],[logseq____"^15logseq____",[228,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[228,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[228,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[228,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[228,logseq____"^Hlogseq____",192,536870923]],[logseq____"^15logseq____",[228,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[228,logseq____"^;logseq____",logseq____"~u6535b15c-03f2-42a9-bd54-f17ea7a86f17logseq____",536870923]],[logseq____"^15logseq____",[229,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870923]],[logseq____"^15logseq____",[229,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[229,logseq____"^Flogseq____",237,536870923]],[logseq____"^15logseq____",[229,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[229,logseq____"^Vlogseq____",188,536870923]],[logseq____"^15logseq____",[229,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[229,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[229,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[229,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[229,logseq____"^Hlogseq____",203,536870923]],[logseq____"^15logseq____",[229,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[229,logseq____"^;logseq____",logseq____"~u6535b15c-6202-4b73-857e-d882e33d98a6logseq____",536870923]],[logseq____"^15logseq____",[230,logseq____"^Qlogseq____",logseq____"Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____",536870923]],[logseq____"^15logseq____",[230,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[230,logseq____"^Flogseq____",229,536870923]],[logseq____"^15logseq____",[230,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[230,logseq____"^Vlogseq____",229,536870923]],[logseq____"^15logseq____",[230,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[230,logseq____"^Ulogseq____",195,536870923]],[logseq____"^15logseq____",[230,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[230,logseq____"^Hlogseq____",195,536870923]],[logseq____"^15logseq____",[230,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[230,logseq____"^;logseq____",logseq____"~u6535b15c-394e-4850-9c60-1065fa44f76dlogseq____",536870923]],[logseq____"^15logseq____",[231,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&\\logseq____"5\\\\text{ ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[231,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[231,logseq____"^Flogseq____",230,536870923]],[logseq____"^15logseq____",[231,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[231,logseq____"^Vlogseq____",229,536870923]],[logseq____"^15logseq____",[231,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[231,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[231,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[231,logseq____"^;logseq____",logseq____"~u6535b15c-881e-499a-b458-db32ec9ac3edlogseq____",536870923]],[logseq____"^15logseq____",[232,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____",536870923]],[logseq____"^15logseq____",[232,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[232,logseq____"^Flogseq____",215,536870923]],[logseq____"^15logseq____",[232,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[232,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",195,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",200,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",202,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",206,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[232,logseq____"^Hlogseq____",195,536870923]],[logseq____"^15logseq____",[232,logseq____"^Hlogseq____",200,536870923]],[logseq____"^15logseq____",[232,logseq____"^Hlogseq____",202,536870923]],[logseq____"^15logseq____",[232,logseq____"^Hlogseq____",206,536870923]],[logseq____"^15logseq____",[232,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[232,logseq____"^;logseq____",logseq____"~u6535b15c-bc02-4b8d-9fc3-cef185076139logseq____",536870923]],[logseq____"^15logseq____",[233,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____",536870923]],[logseq____"^15logseq____",[233,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[233,logseq____"^Flogseq____",216,536870923]],[logseq____"^15logseq____",[233,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[233,logseq____"^Vlogseq____",216,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",199,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",209,536870923]],[logseq____"^15logseq____",[233,logseq____"^Hlogseq____",199,536870923]],[logseq____"^15logseq____",[233,logseq____"^Hlogseq____",205,536870923]],[logseq____"^15logseq____",[233,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[233,logseq____"^;logseq____",logseq____"~u6535b15c-ba23-43d5-8f1c-533e224b6a0blogseq____",536870923]],[logseq____"^15logseq____",[234,logseq____"^Qlogseq____",logseq____"[Variable]([[Variablen]]), die den Wert $w$ oder $f$ 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(logik)logseq____",536870924]],[logseq____"^15logseq____",[263,logseq____"^11logseq____",logseq____"Objekt (Logik)logseq____",536870924]],[logseq____"^15logseq____",[263,logseq____"^Blogseq____",1698017629027,536870924]],[logseq____"^15logseq____",[263,logseq____"^;logseq____",logseq____"~u6535b15d-ff2e-4428-a8cb-05cae0d513e3logseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Qlogseq____",logseq____"Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Flogseq____",269,536870924]],[logseq____"^15logseq____",[264,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[264,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[264,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[264,logseq____"^;logseq____",logseq____"~u6535b15d-7977-4e70-8766-49a5d94ac798logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Qlogseq____",logseq____"Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Flogseq____",267,536870924]],[logseq____"^15logseq____",[265,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[265,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[265,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[265,logseq____"^;logseq____",logseq____"~u6535b15d-0b66-42fd-89bc-ebd9bacc29a4logseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Qlogseq____",logseq____"Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Flogseq____",292,536870924]],[logseq____"^15logseq____",[266,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[266,logseq____"^Vlogseq____",271,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[266,logseq____"^Hlogseq____",251,536870924]],[logseq____"^15logseq____",[266,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[266,logseq____"^;logseq____",logseq____"~u6535b15c-bee6-472e-aceb-4c426102cd88logseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\logseq____"\\\\text{x ist prim}\\logseq____" \\\\quad logseq____& \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____"\\\\underbrace{x}_{x_1}logseq____<\\\\underbrace{y}_{x_2}\\logseq____"\\\\quad logseq____&\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____"\\\\text{x ist wahr}\\logseq____"\\\\quadlogseq____&\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Flogseq____",276,536870924]],[logseq____"^15logseq____",[267,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[267,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[267,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[267,logseq____"^;logseq____",logseq____"~u6535b15d-d690-4a01-a493-b4aa00946d59logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Qlogseq____",logseq____"Wäre $y$ aus $\\\\Reals$ mit $xlogseq____<y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____<y$, Widerspruch. $\\\\blacksquare$logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Flogseq____",300,536870924]],[logseq____"^15logseq____",[268,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[268,logseq____"^Vlogseq____",300,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[268,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[268,logseq____"^;logseq____",logseq____"~u6535b15c-c584-4520-8517-a14651f9277blogseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Qlogseq____",logseq____"Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Flogseq____",265,536870924]],[logseq____"^15logseq____",[269,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[269,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",243,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",262,536870924]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",243,536870924]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",262,536870924]],[logseq____"^15logseq____",[269,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[269,logseq____"^;logseq____",logseq____"~u6535b15d-6b54-449e-af1f-91e01274c997logseq____",536870924]],[logseq____"^15logseq____",[270,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[270,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[270,logseq____"^Flogseq____",272,536870924]],[logseq____"^15logseq____",[270,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[270,logseq____"^Vlogseq____",272,536870924]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[270,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[270,logseq____"^;logseq____",logseq____"~u6535b15c-41f9-4747-a1c3-139e772771d6logseq____",536870924]],[logseq____"^15logseq____",[271,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[271,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[271,logseq____"^Flogseq____",296,536870924]],[logseq____"^15logseq____",[271,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[271,logseq____"^Vlogseq____",296,536870924]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[271,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[271,logseq____"^;logseq____",logseq____"~u6535b15c-e645-4a7a-81b8-e4f53ff33241logseq____",536870924]],[logseq____"^15logseq____",[272,logseq____"^Qlogseq____",logseq____"## [[Regeln]]logseq____",536870924]],[logseq____"^15logseq____",[272,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[272,logseq____"^Flogseq____",297,536870924]],[logseq____"^15logseq____",[272,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[272,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[272,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870924]],[logseq____"^15logseq____",[272,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",239,536870924]],[logseq____"^15logseq____",[272,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[272,logseq____"^;logseq____",logseq____"~u6535b15c-ca88-4119-83f1-16dd9787d636logseq____",536870924]],[logseq____"^15logseq____",[273,logseq____"^Qlogseq____",logseq____"Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____",536870924]],[logseq____"^15logseq____",[273,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[273,logseq____"^Flogseq____",264,536870924]],[logseq____"^15logseq____",[273,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[273,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[273,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[273,logseq____"^;logseq____",logseq____"~u6535b15d-bd9b-4fba-a001-98619e38df70logseq____",536870924]],[logseq____"^15logseq____",[274,logseq____"^Qlogseq____",logseq____"see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____",536870924]],[logseq____"^15logseq____",[274,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[274,logseq____"^Flogseq____",277,536870924]],[logseq____"^15logseq____",[274,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[274,logseq____"^Vlogseq____",277,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",240,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",245,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",248,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",249,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",255,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",256,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",240,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",245,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",248,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",249,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",255,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",256,536870924]],[logseq____"^15logseq____",[274,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[274,logseq____"^;logseq____",logseq____"~u6535b15d-c1ba-4e61-ad89-a8974bc35429logseq____",536870924]],[logseq____"^15logseq____",[275,logseq____"^Qlogseq____",logseq____"#FIXMElogseq____",536870924]],[logseq____"^15logseq____",[275,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[275,logseq____"^Flogseq____",297,536870924]],[logseq____"^15logseq____",[275,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[275,logseq____"^Vlogseq____",297,536870924]],[logseq____"^15logseq____",[275,logseq____"^Ulogseq____",43,536870924]],[logseq____"^15logseq____",[275,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[275,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[275,logseq____"^Hlogseq____",43,536870924]],[logseq____"^15logseq____",[275,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[275,logseq____"^;logseq____",logseq____"~u6535b15c-be1f-4bb3-ae1e-5134aaa6f13flogseq____",536870924]],[logseq____"^15logseq____",[276,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870924]],[logseq____"^15logseq____",[276,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[276,logseq____"^Flogseq____",291,536870924]],[logseq____"^15logseq____",[276,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[276,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[276,logseq____"^Hlogseq____",36,536870924]],[logseq____"^15logseq____",[276,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[276,logseq____"^;logseq____",logseq____"~u6535b15d-c790-4c9f-bf3f-d8b3021c5668logseq____",536870924]],[logseq____"^15logseq____",[277,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&\\\\equiv p, \\\\quad \\\\neg logseq____&\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[277,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[277,logseq____"^Flogseq____",287,536870924]],[logseq____"^15logseq____",[277,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[277,logseq____"^Vlogseq____",246,536870924]],[logseq____"^15logseq____",[277,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[277,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[277,logseq____"^;logseq____",logseq____"~u6535b15d-ab4d-400d-bef4-39d06c82680dlogseq____",536870924]],[logseq____"^15logseq____",[278,logseq____"^Qlogseq____",logseq____"see: [[Allquantor]] [[Existenzquantor]]logseq____",536870924]],[logseq____"^15logseq____",[278,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[278,logseq____"^Flogseq____",285,536870924]],[logseq____"^15logseq____",[278,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[278,logseq____"^Vlogseq____",285,536870924]],[logseq____"^15logseq____",[278,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[278,logseq____"^Ulogseq____",252,536870924]],[logseq____"^15logseq____",[278,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[278,logseq____"^Ulogseq____",258,536870924]],[logseq____"^15logseq____",[278,logseq____"^Hlogseq____",252,536870924]],[logseq____"^15logseq____",[278,logseq____"^Hlogseq____",258,536870924]],[logseq____"^15logseq____",[278,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[278,logseq____"^;logseq____",logseq____"~u6535b15d-cacb-4cea-a00d-a53a3ba758f2logseq____",536870924]],[logseq____"^15logseq____",[279,logseq____"^Qlogseq____",logseq____"$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, logseq____",536870924]],[logseq____"^15logseq____",[279,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[279,logseq____"^Flogseq____",280,536870924]],[logseq____"^15logseq____",[279,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[279,logseq____"^Vlogseq____",280,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",241,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",244,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[279,logseq____"^Hlogseq____",241,536870924]],[logseq____"^15logseq____",[279,logseq____"^Hlogseq____",244,536870924]],[logseq____"^15logseq____",[279,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[279,logseq____"^;logseq____",logseq____"~u6535b15c-4262-4719-bb5c-0071158f747alogseq____",536870924]],[logseq____"^15logseq____",[280,logseq____"^Qlogseq____",logseq____"Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____<x+1=y$ also $xlogseq____<y$. $\\\\blacksquare$logseq____",536870924]],[logseq____"^15logseq____",[280,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[280,logseq____"^Flogseq____",299,536870924]],[logseq____"^15logseq____",[280,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[280,logseq____"^Vlogseq____",299,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[280,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[280,logseq____"^;logseq____",logseq____"~u6535b15c-5174-447d-be84-b1567e2c1c0elogseq____",536870924]],[logseq____"^15logseq____",[281,logseq____"^Qlogseq____",logseq____"see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____",536870924]],[logseq____"^15logseq____",[281,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[281,logseq____"^Flogseq____",270,536870924]],[logseq____"^15logseq____",[281,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[281,logseq____"^Vlogseq____",270,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",242,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",254,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",259,536870924]],[logseq____"^15logseq____",[281,logseq____"^Hlogseq____",242,536870924]],[logseq____"^15logseq____",[281,logseq____"^Hlogseq____",254,536870924]],[logseq____"^15logseq____",[281,logseq____"^Hlogseq____",259,536870924]],[logseq____"^15logseq____",[281,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[281,logseq____"^;logseq____",logseq____"~u6535b15c-440a-4abe-8b67-cf6e3c4980cdlogseq____",536870924]],[logseq____"^15logseq____",[282,logseq____"^Qlogseq____",logseq____"[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____",536870924]],[logseq____"^15logseq____",[282,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[282,logseq____"^Flogseq____",286,536870924]],[logseq____"^15logseq____",[282,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[282,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[282,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[282,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[282,logseq____"^Ulogseq____",261,536870924]],[logseq____"^15logseq____",[282,logseq____"^Hlogseq____",257,536870924]],[logseq____"^15logseq____",[282,logseq____"^Hlogseq____",261,536870924]],[logseq____"^15logseq____",[282,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[282,logseq____"^;logseq____",logseq____"~u6535b15d-63f9-48ec-8de5-adb7facac00alogseq____",536870924]],[logseq____"^15logseq____",[283,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870924]],[logseq____"^15logseq____",[283,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[283,logseq____"^Flogseq____",296,536870924]],[logseq____"^15logseq____",[283,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[283,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[283,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[283,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[283,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[283,logseq____"^Hlogseq____",36,536870924]],[logseq____"^15logseq____",[283,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[283,logseq____"^;logseq____",logseq____"~u6535b15c-490a-4ccd-83cc-ea75c6caa464logseq____",536870924]],[logseq____"^15logseq____",[284,logseq____"^Qlogseq____",logseq____"Nach Ersetzung von $x$ in der AF $\\logseq____"xlogseq____<y\\logseq____"$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____"17logseq____<y\\logseq____"$logseq____",536870924]],[logseq____"^15logseq____",[284,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[284,logseq____"^Flogseq____",267,536870924]],[logseq____"^15logseq____",[284,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[284,logseq____"^Vlogseq____",267,536870924]],[logseq____"^15logseq____",[284,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[284,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[284,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[284,logseq____"^;logseq____",logseq____"~u6535b15d-450a-49a9-8c18-cf812a1dfdbalogseq____",536870924]],[logseq____"^15logseq____",[285,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[285,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[285,logseq____"^Flogseq____",273,536870924]],[logseq____"^15logseq____",[285,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[285,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[285,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[285,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[285,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[285,logseq____"^;logseq____",logseq____"~u6535b15d-6d72-4cd5-b5ba-3514a1f17015logseq____",536870924]],[logseq____"^15logseq____",[286,logseq____"^Qlogseq____",logseq____"# [[Aussageform]]logseq____",536870924]],[logseq____"^15logseq____",[286,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[286,logseq____"^Flogseq____",277,536870924]],[logseq____"^15logseq____",[286,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[286,logseq____"^Vlogseq____",246,536870924]],[logseq____"^15logseq____",[286,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[286,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[286,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870924]],[logseq____"^15logseq____",[286,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[286,logseq____"^Hlogseq____",257,536870924]],[logseq____"^15logseq____",[286,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[286,logseq____"^;logseq____",logseq____"~u6535b15d-8889-4489-ad93-5efb100263ealogseq____",536870924]],[logseq____"^15logseq____",[287,logseq____"^Qlogseq____",logseq____"# [[Regeln]]logseq____",536870924]],[logseq____"^15logseq____",[287,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[287,logseq____"^Flogseq____",246,536870924]],[logseq____"^15logseq____",[287,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[287,logseq____"^Vlogseq____",246,536870924]],[logseq____"^15logseq____",[287,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[287,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[287,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870924]],[logseq____"^15logseq____",[287,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[287,logseq____"^Hlogseq____",239,536870924]],[logseq____"^15logseq____",[287,logseq____"^17logseq____",false,536870924]],[logseq____"^15logseq____",[287,logseq____"^;logseq____",logseq____"~u6535b15d-0be5-41e6-baa3-4392875b72aalogseq____",536870924]],[logseq____"^15logseq____",[288,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870924]],[logseq____"^15logseq____",[288,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[288,logseq____"^Flogseq____",271,536870924]],[logseq____"^15logseq____",[288,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[288,logseq____"^Vlogseq____",296,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[288,logseq____"^Hlogseq____",36,536870924]],[logseq____"^15logseq____",[288,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[288,logseq____"^;logseq____",logseq____"~u6535b15c-d1c8-4dae-8a26-6027d9a26b83logseq____",536870924]],[logseq____"^15logseq____",[289,logseq____"^Qlogseq____",logseq____"$\\\\exists x:p(x)$ ist die Aussage: \\logseq____"Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____",536870924]],[logseq____"^15logseq____",[289,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[289,logseq____"^Flogseq____",285,536870924]],[logseq____"^15logseq____",[289,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[289,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[289,logseq____"^Ulogseq____",195,536870924]],[logseq____"^15logseq____",[289,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[289,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[289,logseq____"^Hlogseq____",195,536870924]],[logseq____"^15logseq____",[289,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[289,logseq____"^;logseq____",logseq____"~u6535b15d-8f46-431e-a8bc-32d16f586f5clogseq____",536870924]],[logseq____"^15logseq____",[290,logseq____"^Qlogseq____",logseq____"Betrachte $\\logseq____"xlogseq____<y\\logseq____"$ als AF über $\\\\Reals, \\\\Reals$logseq____",536870924]],[logseq____"^15logseq____",[290,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[290,logseq____"^Flogseq____",288,536870924]],[logseq____"^15logseq____",[290,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[290,logseq____"^Vlogseq____",288,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[290,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[290,logseq____"^;logseq____",logseq____"~u6535b15c-c9c2-4644-8a5b-c52184b33b4dlogseq____",536870924]],[logseq____"^15logseq____",[291,logseq____"^Qlogseq____",logseq____"[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____",536870924]],[logseq____"^15logseq____",[291,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[291,logseq____"^Flogseq____",282,536870924]],[logseq____"^15logseq____",[291,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[291,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",199,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",203,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",260,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",263,536870924]],[logseq____"^15logseq____",[291,logseq____"^Hlogseq____",199,536870924]],[logseq____"^15logseq____",[291,logseq____"^Hlogseq____",203,536870924]],[logseq____"^15logseq____",[291,logseq____"^Hlogseq____",260,536870924]],[logseq____"^15logseq____",[291,logseq____"^Hlogseq____",263,536870924]],[logseq____"^15logseq____",[291,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[291,logseq____"^;logseq____",logseq____"~u6535b15d-7ebf-481d-becc-f864a19eb405logseq____",536870924]],[logseq____"^15logseq____",[292,logseq____"^Qlogseq____",logseq____"wobei $\\\\pi$ eine \\logseq____"[[Permutation]]\\logseq____" der Zahl $(1,2,\\\\cdots,n)$ istlogseq____",536870924]],[logseq____"^15logseq____",[292,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[292,logseq____"^Flogseq____",271,536870924]],[logseq____"^15logseq____",[292,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[292,logseq____"^Vlogseq____",271,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",253,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[292,logseq____"^Hlogseq____",253,536870924]],[logseq____"^15logseq____",[292,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[292,logseq____"^;logseq____",logseq____"~u6535b15c-3fe9-4ce0-a476-305ff299fedclogseq____",536870924]],[logseq____"^15logseq____",[293,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow 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<script>window.logseq_state="{:ui/theme \"dark\", :config {\"local\" {:shortcuts {}, :default-templates {:journals \"\"}, :feature/enable-journals? false, :query/views {:pprint (fn [r] [:pre.code (pprint r)])}, :editor/preferred-pasting-file? true, :macros {}, :shortcut/doc-mode-enter-for-new-block? false, :favorites [], :ui/show-empty-bullets? false, :file/name-format :triple-lowbar, :preferred-workflow :now, :publishing/all-pages-public? true, :ref/default-open-blocks-level 2, :feature/enable-block-timestamps? false, :start-of-week 6, :ref/linked-references-collapsed-threshold 50, :outliner/block-title-collapse-enabled? false, :commands [], :ui/show-full-blocks? false, :meta/version 1, :hidden [], :default-queries {:journals [{:title \"🔨 NOW\", :query [:find (pull ?h [*]) :in $ ?start ?today :where [?h :block/marker ?marker] [(contains? #{\"NOW\" \"DOING\"} ?marker)] [?h :block/page ?p] [?p :block/journal? true] [?p :block/journal-day ?d] [(>= ?d ?start)] [(<= ?d ?today)]], :inputs [:14d :today], :result-transform (fn [result] (sort-by (fn [h] (get h :block/priority \"Z\")) result)), :group-by-page? false, :collapsed? false} {:title \"📅 NEXT\", :query [:find (pull ?h [*]) :in $ ?start ?next :where [?h :block/marker ?marker] [(contains? #{\"NOW\" \"LATER\" \"TODO\"} ?marker)] [?h :block/page ?p] [?p :block/journal? true] [?p :block/journal-day ?d] [(> ?d ?start)] [(< ?d ?next)]], :inputs [:today :7d-after], :group-by-page? false, :collapsed? false}]}, :ui/auto-expand-block-refs? true, :ui/enable-tooltip? true, :query/result-transforms {:sort-by-priority (fn [result] (sort-by (fn [h] (get h :block/priority \"Z\")) result))}, :property-pages/enabled? true, :block/content-max-length 10000, :ui/show-command-doc? true, :feature/enable-search-remove-accents? true, :default-home {:page \"Vorlesungs Notizen\"}}}}"</script>
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<script type="text/javascript">// Single Page Apps for GitHub Pages
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// https://github.com/rafgraph/spa-github-pages
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// Copyright (c) 2016 Rafael Pedicini, licensed under the MIT License
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// ----------------------------------------------------------------------
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// This script checks to see if a redirect is present in the query string
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// and converts it back into the correct url and adds it to the
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// browser's history using window.history.replaceState(...),
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// which won't cause the browser to attempt to load the new url.
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// When the single page app is loaded further down in this file,
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// the correct url will be waiting in the browser's history for
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// the single page app to route accordingly.
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(function(l) {
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if (l.search) {
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var q = {};
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l.search.slice(1).split('&').forEach(function(v) {
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var a = v.split('=');
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q[a[0]] = a.slice(1).join('=').replace(/~and~/g, '&');
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});
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if (q.p !== undefined) {
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window.history.replaceState(null, null,
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l.pathname.slice(0, -1) + (q.p || '') +
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(q.q ? ('?' + q.q) : '') +
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l.hash
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);
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}
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}
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}(window.location))</script>
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<script src="static/js/main.js"></script>
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<script src="static/js/interact.min.js"></script>
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<script src="static/js/highlight.min.js"></script>
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<script src="static/js/katex.min.js"></script>
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<script src="static/js/html2canvas.min.js"></script>
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<script src="static/js/code-editor.js"></script>
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<script src="static/js/custom.js"></script>
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</body>
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