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\\\\\\\\\\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____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",89,536870919]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",89,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",33,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[53,logseq____"^Hlogseq____",33,536870919]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u65296c00-a877-4166-b3e9-bf688c840c1clogseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"# [[Wurzelgleichung]]logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",56,536870919]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",74,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[54,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",30,536870919]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u65296c00-9749-4eb2-9afc-cd00e82eb460logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"https://www.wolframalpha.comlogseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",71,536870919]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",71,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",46,536870919]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u65296c00-0426-47b0-9cfa-d2b725ed8426logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",69,536870919]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",74,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[56,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",29,536870919]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u65296c00-aad5-4462-804a-17a4019853c3logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",87,536870919]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",58,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[57,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",28,536870919]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u65296c00-29cc-4da4-b8b8-711c72932df7logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",104,536870919]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[58,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",34,536870919]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u65296c00-45fc-4976-8c69-80c72ac97f51logseq____",536870919]],[logseq____"^15logseq____",[59,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____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",50,536870919]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",50,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u65296c00-8ba5-4cc7-81c9-96fa1ca6b6aelogseq____",536870919]],[logseq____"^15logseq____",[60,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____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",104,536870919]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",104,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u65296c00-5dd7-4660-996e-7c594c3bcec2logseq____",536870919]],[logseq____"^15logseq____",[61,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____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",76,536870919]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",73,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u65296c00-55cd-4b98-a0e8-eb416654641dlogseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",61,536870919]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",61,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u65296c00-3088-4923-b648-9e986a6670d7logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",65,536870919]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u65296c00-c0cb-49aa-b65f-bac70c77421elogseq____",536870919]],[logseq____"^15logseq____",[64,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____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",91,536870919]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",92,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u65296c00-b953-4976-a898-003fdc3ad1bdlogseq____",536870919]],[logseq____"^15logseq____",[65,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____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",97,536870919]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u65296c00-5b2a-4f6f-9efa-de0929fde885logseq____",536870919]],[logseq____"^15logseq____",[66,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____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",88,536870919]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",88,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u65296c00-2684-46b8-8362-df82ae11c8calogseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",59,536870919]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",50,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u65296c00-2c76-42ea-93d7-8c0477192081logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",66,536870919]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",88,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[68,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u65296c00-5436-4f52-babe-2b5faef7c94alogseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",73,536870919]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",74,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[69,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[69,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[69,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u65296c00-dd1e-4c3c-bcfe-08a139b70387logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",97,536870919]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",57,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[70,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[70,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[70,logseq____"^Hlogseq____",32,536870919]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u65296c00-3b2a-479e-a8f5-59607e07f86dlogseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",99,536870919]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",99,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",46,536870919]],[logseq____"^15logseq____",[71,logseq____"^Hlogseq____",46,536870919]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u65296c00-a61e-4bb3-8808-909627397dd8logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Qlogseq____",logseq____"Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",83,536870919]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",54,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u65296c00-5156-4d1b-9419-3b4f21c0b4d1logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",74,536870919]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",74,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[73,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[73,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[73,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u65296c00-6998-4858-afef-5075b2629d65logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",58,536870919]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[74,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[74,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u65296c00-08e7-463d-bded-58c6ea334be4logseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",69,536870919]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",69,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u65296c00-6795-4750-90ac-24216f0d70f4logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",49,536870919]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",73,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[76,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u65296c00-f667-463c-8da8-bd48061b6bd0logseq____",536870919]],[logseq____"^15logseq____",[77,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____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",102,536870919]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",102,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u65296c00-62b0-4778-a401-5c62f87f4cf5logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",85,536870919]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",70,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u65296c00-b71a-4fea-8b5d-49d7bed8218flogseq____",536870919]],[logseq____"^15logseq____",[79,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____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",48,536870919]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",48,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u65296c00-c388-4fa8-96b4-c60c5fdfe572logseq____",536870919]],[logseq____"^15logseq____",[80,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____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",88,536870919]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",69,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u65296c00-8a3c-4360-9c30-ce7bf470ded8logseq____",536870919]],[logseq____"^15logseq____",[81,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____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",47,536870919]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",93,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[81,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u65296c00-0ec2-4909-944c-edab5cf78fablogseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&=a^2+2ab+b^2logseq____&,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&=a^2-2ab+b^2logseq____&,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&=a^2-b^2logseq____&,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Flogseq____",58,536870919]],[logseq____"^15logseq____",[82,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[82,logseq____"^Vlogseq____",58,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[82,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u65296c00-f055-4072-b500-be7fc9e74d45logseq____",536870919]],[logseq____"^15logseq____",[83,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 x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",54,536870919]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",54,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u65296c00-81a5-4f90-ae74-65fff0485891logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",89,536870919]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[84,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",31,536870919]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u65296c00-3d72-40f4-ad65-f3269df1ec8flogseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",70,536870919]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",70,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",38,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^Hlogseq____",38,536870919]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u65296c00-bf13-4978-9bae-65147cfc9deblogseq____",536870919]],[logseq____"^15logseq____",[86,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____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",84,536870919]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u65296c00-dc4b-41f0-b440-701c0a99f406logseq____",536870919]],[logseq____"^15logseq____",[87,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____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",82,536870919]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",58,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u65296c00-8cc0-47a9-abd0-2b2b9d906511logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",51,536870919]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",69,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u65296c00-2664-421d-a20a-d99fb034a10blogseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",99,536870919]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[89,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[89,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u65296c00-74a1-4210-bd81-2367ca4df40elogseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",53,536870919]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",89,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u65296c00-1ad5-4e8a-b4c4-ea1e8f22b5ealogseq____",536870919]],[logseq____"^15logseq____",[91,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____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",92,536870919]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",92,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",26,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[91,logseq____"^Hlogseq____",26,536870919]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u65296c00-758f-4bbd-afce-ebd09b617fb6logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",100,536870919]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",56,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[92,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[92,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[92,logseq____"^Hlogseq____",43,536870919]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u65296c00-8055-4b40-b5b6-c6ed0710aa06logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",84,536870919]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[93,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[93,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u65296c00-94f6-495e-ae4e-54ec123fb6c6logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&=a^2-b^2\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",76,536870919]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",76,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u65296c00-319e-4936-9b39-c74287bcbaa0logseq____",536870919]],[logseq____"^15logseq____",[95,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____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",60,536870919]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",104,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u65296c00-2d56-456d-aa23-f595821400fdlogseq____",536870919]],[logseq____"^15logseq____",[96,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____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Flogseq____",67,536870919]],[logseq____"^15logseq____",[96,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[96,logseq____"^Vlogseq____",67,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[96,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[96,logseq____"^;logseq____",logseq____"~u65296c00-4293-4b7c-9250-f7202f25072alogseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Flogseq____",52,536870919]],[logseq____"^15logseq____",[97,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[97,logseq____"^Vlogseq____",57,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[97,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[97,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[97,logseq____"^;logseq____",logseq____"~u65296c00-f33f-4992-9f3d-99cdf844cf24logseq____",536870919]],[logseq____"^15logseq____",[98,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&=x^2\\\\\\\\\\ny^2-34y+225logseq____&=0\\\\\\\\\\ny_{1,2}logseq____&=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&\\\\rightarrow logseq____&x_1=5;logseq____&x_2=-5\\\\\\\\\\nx^2=9logseq____&\\\\rightarrow logseq____&x_1=3;logseq____&x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[98,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[98,logseq____"^Flogseq____",64,536870919]],[logseq____"^15logseq____",[98,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[98,logseq____"^Vlogseq____",92,536870919]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[98,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[98,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[98,logseq____"^;logseq____",logseq____"~u65296c00-d8df-46a4-a453-b363b8a4a55flogseq____",536870919]],[logseq____"^15logseq____",[99,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870919]],[logseq____"^15logseq____",[99,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[99,logseq____"^Flogseq____",40,536870919]],[logseq____"^15logseq____",[99,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[99,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[99,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[99,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[99,logseq____"^Hlogseq____",44,536870919]],[logseq____"^15logseq____",[99,logseq____"^17logseq____",false,536870919]],[logseq____"^15logseq____",[99,logseq____"^;logseq____",logseq____"~u65296c00-fb4c-49af-bfbd-a46558161bb7logseq____",536870919]],[logseq____"^15logseq____",[100,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____",536870919]],[logseq____"^15logseq____",[100,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[100,logseq____"^Flogseq____",56,536870919]],[logseq____"^15logseq____",[100,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[100,logseq____"^Vlogseq____",56,536870919]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[100,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[100,logseq____"^;logseq____",logseq____"~u65296c00-9a8f-4bd9-a9d6-e380d6683255logseq____",536870919]],[logseq____"^15logseq____",[101,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870919]],[logseq____"^15logseq____",[101,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[101,logseq____"^Flogseq____",95,536870919]],[logseq____"^15logseq____",[101,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[101,logseq____"^Vlogseq____",95,536870919]],[logseq____"^15logseq____",[101,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[101,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[101,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[101,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[101,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[101,logseq____"^;logseq____",logseq____"~u65296c00-8ef2-4a06-8a5b-65cec95f098dlogseq____",536870919]],[logseq____"^15logseq____",[102,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870919]],[logseq____"^15logseq____",[102,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[102,logseq____"^Flogseq____",64,536870919]],[logseq____"^15logseq____",[102,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[102,logseq____"^Vlogseq____",64,536870919]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[102,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[102,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[102,logseq____"^;logseq____",logseq____"~u65296c00-be89-4356-a432-b44fa6892d03logseq____",536870919]],[logseq____"^15logseq____",[103,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&= \\\\frac1{\\\\ln a}\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[103,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[103,logseq____"^Flogseq____",86,536870919]],[logseq____"^15logseq____",[103,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[103,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[103,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[103,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[103,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[103,logseq____"^;logseq____",logseq____"~u65296c00-5b51-4545-ae55-c335147fb026logseq____",536870919]],[logseq____"^15logseq____",[104,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870919]],[logseq____"^15logseq____",[104,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[104,logseq____"^Flogseq____",48,536870919]],[logseq____"^15logseq____",[104,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[104,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[104,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[104,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[104,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[104,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[104,logseq____"^;logseq____",logseq____"~u65296c00-0be2-4e5f-8133-f4fb3eedc3adlogseq____",536870919]],[logseq____"^15logseq____",[106,logseq____"^Klogseq____",1697213440941,536870920]],[logseq____"^15logseq____",[106,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[106,logseq____"^Ylogseq____",logseq____"kreislogseq____",536870920]],[logseq____"^15logseq____",[106,logseq____"^11logseq____",logseq____"Kreislogseq____",536870920]],[logseq____"^15logseq____",[106,logseq____"^Blogseq____",1697213440941,536870920]],[logseq____"^15logseq____",[106,logseq____"^;logseq____",logseq____"~u65296c00-9e4a-40e8-a773-e201f1f38429logseq____",536870920]],[logseq____"^15logseq____",[107,logseq____"^Klogseq____",1697213440939,536870920]],[logseq____"^15logseq____",[107,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[107,logseq____"^Ylogseq____",logseq____"fallunterscheidunglogseq____",536870920]],[logseq____"^15logseq____",[107,logseq____"^11logseq____",logseq____"Fallunterscheidunglogseq____",536870920]],[logseq____"^15logseq____",[107,logseq____"^Blogseq____",1697213440939,536870920]],[logseq____"^15logseq____",[107,logseq____"^;logseq____",logseq____"~u65296c00-5e9e-4087-a5b0-f12f73b9f067logseq____",536870920]],[logseq____"^15logseq____",[108,logseq____"^Klogseq____",1697213440937,536870920]],[logseq____"^15logseq____",[108,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[108,logseq____"^Ylogseq____",logseq____"ungleichungenlogseq____",536870920]],[logseq____"^15logseq____",[108,logseq____"^11logseq____",logseq____"Ungleichungenlogseq____",536870920]],[logseq____"^15logseq____",[108,logseq____"^Blogseq____",1697213440937,536870920]],[logseq____"^15logseq____",[108,logseq____"^;logseq____",logseq____"~u65296c01-f824-4602-91ea-d44498024a3flogseq____",536870929]],[logseq____"^15logseq____",[109,logseq____"^Klogseq____",1697213440933,536870920]],[logseq____"^15logseq____",[109,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[109,logseq____"^Ylogseq____",logseq____"lösungsmengenlogseq____",536870920]],[logseq____"^15logseq____",[109,logseq____"^11logseq____",logseq____"Lösungsmengenlogseq____",536870920]],[logseq____"^15logseq____",[109,logseq____"^Blogseq____",1697213440933,536870920]],[logseq____"^15logseq____",[109,logseq____"^;logseq____",logseq____"~u65296c00-df2f-4443-a733-7305aa22a540logseq____",536870920]],[logseq____"^15logseq____",[110,logseq____"^Klogseq____",1697213440935,536870920]],[logseq____"^15logseq____",[110,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[110,logseq____"^Ylogseq____",logseq____"abstandlogseq____",536870920]],[logseq____"^15logseq____",[110,logseq____"^11logseq____",logseq____"Abstandlogseq____",536870920]],[logseq____"^15logseq____",[110,logseq____"^Blogseq____",1697213440935,536870920]],[logseq____"^15logseq____",[110,logseq____"^;logseq____",logseq____"~u65296c00-729a-4bff-aae5-5e6bf9e9cd4dlogseq____",536870920]],[logseq____"^15logseq____",[111,logseq____"^Klogseq____",1697213440937,536870920]],[logseq____"^15logseq____",[111,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[111,logseq____"^Ylogseq____",logseq____"betraglogseq____",536870920]],[logseq____"^15logseq____",[111,logseq____"^11logseq____",logseq____"Betraglogseq____",536870920]],[logseq____"^15logseq____",[111,logseq____"^Blogseq____",1697213440937,536870920]],[logseq____"^15logseq____",[111,logseq____"^;logseq____",logseq____"~u65296c00-22cb-4ca9-9b02-17cf6ee5bee8logseq____",536870920]],[logseq____"^15logseq____",[112,logseq____"^Klogseq____",1697213440939,536870920]],[logseq____"^15logseq____",[112,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[112,logseq____"^Ylogseq____",logseq____"auffrischung mathematik/23-10-05logseq____",536870920]],[logseq____"^15logseq____",[112,logseq____"^Alogseq____",23,536870920]],[logseq____"^15logseq____",[112,logseq____"^11logseq____",logseq____"Auffrischung Mathematik/23-10-05logseq____",536870920]],[logseq____"^15logseq____",[112,logseq____"^Blogseq____",1697213440939,536870920]],[logseq____"^15logseq____",[112,logseq____"^;logseq____",logseq____"~u65296c00-069a-43af-826d-2e399061794clogseq____",536870920]],[logseq____"^15logseq____",[113,logseq____"^Klogseq____",1697213440936,536870920]],[logseq____"^15logseq____",[113,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[113,logseq____"^Ylogseq____",logseq____"betragsungleichungenlogseq____",536870920]],[logseq____"^15logseq____",[113,logseq____"^11logseq____",logseq____"Betragsungleichungenlogseq____",536870920]],[logseq____"^15logseq____",[113,logseq____"^Blogseq____",1697213440936,536870920]],[logseq____"^15logseq____",[113,logseq____"^;logseq____",logseq____"~u65296c00-1e29-408b-9395-4fe8756de179logseq____",536870920]],[logseq____"^15logseq____",[114,logseq____"^Klogseq____",1697213440933,536870920]],[logseq____"^15logseq____",[114,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[114,logseq____"^Ylogseq____",logseq____"mengenlogseq____",536870920]],[logseq____"^15logseq____",[114,logseq____"^11logseq____",logseq____"Mengenlogseq____",536870920]],[logseq____"^15logseq____",[114,logseq____"^Blogseq____",1697213440933,536870920]],[logseq____"^15logseq____",[114,logseq____"^;logseq____",logseq____"~u65296c00-748e-4089-a0cb-e60599467127logseq____",536870920]],[logseq____"^15logseq____",[115,logseq____"^Qlogseq____",logseq____"Menge aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____<xlogseq____<4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes interval}\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[115,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[115,logseq____"^Flogseq____",155,536870920]],[logseq____"^15logseq____",[115,logseq____"^Xlogseq____",112,536870920]],[logseq____"^15logseq____",[115,logseq____"^Vlogseq____",138,536870920]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",112,536870920]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[115,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[115,logseq____"^;logseq____",logseq____"~u65296c00-2d5f-4625-804a-a7f827f7c82blogseq____",536870920]],[logseq____"^15logseq____",[116,logseq____"^Qlogseq____",logseq____"### Lösung mit [[Fallunterscheidung]]logseq____",536870920]],[logseq____"^15logseq____",[116,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[116,logseq____"^Flogseq____",127,536870920]],[logseq____"^15logseq____",[116,logseq____"^Xlogseq____",112,536870920]],[logseq____"^15logseq____",[116,logseq____"^Vlogseq____",127,536870920]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",107,536870920]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",111,536870920]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",112,536870920]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[116,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870920]],[logseq____"^15logseq____",[116,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[116,logseq____"^Hlogseq____",107,536870920]],[logseq____"^15logseq____",[116,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[116,logseq____"^;logseq____",logseq____"~u65296c00-1f7c-45ec-9ec7-87105e7c81d0logseq____",536870920]],[logseq____"^15logseq____",[117,logseq____"^Qlogseq____",logseq____"#FIXME 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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____",536870922]],[logseq____"^15logseq____",[186,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[186,logseq____"^Flogseq____",189,536870922]],[logseq____"^15logseq____",[186,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[186,logseq____"^Vlogseq____",188,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[186,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[186,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[186,logseq____"^;logseq____",logseq____"~u65296c01-54ec-4750-a97c-a5e2eeb426ddlogseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Flogseq____",183,536870922]],[logseq____"^15logseq____",[187,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[187,logseq____"^Vlogseq____",183,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[187,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[187,logseq____"^;logseq____",logseq____"~u65296c01-ab5c-467f-967b-017834a64163logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Flogseq____",181,536870922]],[logseq____"^15logseq____",[188,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[188,logseq____"^Vlogseq____",199,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[188,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[188,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[188,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[188,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[188,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[188,logseq____"^;logseq____",logseq____"~u65296c01-548a-4150-8bac-d2c240ebe5e1logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Flogseq____",188,536870922]],[logseq____"^15logseq____",[189,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[189,logseq____"^Vlogseq____",188,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",166,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",173,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",165,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",166,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",173,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[189,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[189,logseq____"^;logseq____",logseq____"~u65296c01-fba1-4d2e-9f4f-610855cbcad0logseq____",536870922]],[logseq____"^15logseq____",[190,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____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Flogseq____",203,536870922]],[logseq____"^15logseq____",[190,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[190,logseq____"^Vlogseq____",203,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[190,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[190,logseq____"^;logseq____",logseq____"~u65296c01-5cac-4b1d-acf4-7d4590b61517logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Flogseq____",181,536870922]],[logseq____"^15logseq____",[191,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[191,logseq____"^Vlogseq____",181,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",170,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[191,logseq____"^Hlogseq____",170,536870922]],[logseq____"^15logseq____",[191,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[191,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[191,logseq____"^;logseq____",logseq____"~u65296c01-b5c5-4098-8ba7-82773668653elogseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Flogseq____",194,536870922]],[logseq____"^15logseq____",[192,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[192,logseq____"^Vlogseq____",199,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",179,536870922]],[logseq____"^15logseq____",[192,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[192,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[192,logseq____"^Hlogseq____",179,536870922]],[logseq____"^15logseq____",[192,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[192,logseq____"^;logseq____",logseq____"~u65296c01-2fa2-448d-aa8f-0a65649654c0logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Flogseq____",206,536870922]],[logseq____"^15logseq____",[193,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[193,logseq____"^Vlogseq____",206,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",42,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",175,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[193,logseq____"^Hlogseq____",42,536870922]],[logseq____"^15logseq____",[193,logseq____"^Hlogseq____",175,536870922]],[logseq____"^15logseq____",[193,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[193,logseq____"^;logseq____",logseq____"~u65296c01-1aee-4c36-88fe-1af47742096flogseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Flogseq____",183,536870922]],[logseq____"^15logseq____",[194,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[194,logseq____"^Vlogseq____",199,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",169,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[194,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[194,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[194,logseq____"^Hlogseq____",169,536870922]],[logseq____"^15logseq____",[194,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[194,logseq____"^;logseq____",logseq____"~u65296c01-0711-4c2c-b2a4-e835a64068c2logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Flogseq____",202,536870922]],[logseq____"^15logseq____",[195,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[195,logseq____"^Vlogseq____",202,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",167,536870922]],[logseq____"^15logseq____",[195,logseq____"^Hlogseq____",167,536870922]],[logseq____"^15logseq____",[195,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[195,logseq____"^;logseq____",logseq____"~u65296c01-1b21-41da-8cdb-b24b21cbd49blogseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Flogseq____",192,536870922]],[logseq____"^15logseq____",[196,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[196,logseq____"^Vlogseq____",199,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[196,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[196,logseq____"^;logseq____",logseq____"~u65296c01-8bfc-4f2f-87ac-3f7c5f68295alogseq____",536870922]],[logseq____"^15logseq____",[197,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____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Flogseq____",198,536870922]],[logseq____"^15logseq____",[197,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[197,logseq____"^Vlogseq____",198,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",166,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[197,logseq____"^Hlogseq____",166,536870922]],[logseq____"^15logseq____",[197,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[197,logseq____"^;logseq____",logseq____"~u65296c01-00eb-4f58-bfa7-363e146aa5c9logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Flogseq____",202,536870922]],[logseq____"^15logseq____",[198,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[198,logseq____"^Vlogseq____",159,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[198,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[198,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[198,logseq____"^Hlogseq____",174,536870922]],[logseq____"^15logseq____",[198,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[198,logseq____"^;logseq____",logseq____"~u65296c01-2c8a-45e1-ac7b-e4afd146359blogseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Flogseq____",207,536870922]],[logseq____"^15logseq____",[199,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[199,logseq____"^Vlogseq____",198,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[199,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870922]],[logseq____"^15logseq____",[199,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[199,logseq____"^Hlogseq____",178,536870922]],[logseq____"^15logseq____",[199,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[199,logseq____"^;logseq____",logseq____"~u65296c01-8563-428d-9bf8-43218c35235dlogseq____",536870922]],[logseq____"^15logseq____",[200,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 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[[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Flogseq____",185,536870922]],[logseq____"^15logseq____",[206,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[206,logseq____"^Vlogseq____",199,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[206,logseq____"^?logseq____",[logseq____"^ 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x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist 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Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____",536870923]],[logseq____"^15logseq____",[241,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[241,logseq____"^Flogseq____",258,536870923]],[logseq____"^15logseq____",[241,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[241,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[241,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[241,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[241,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[241,logseq____"^;logseq____",logseq____"~u65296c01-8451-4323-93b8-365a347e8720logseq____",536870923]],[logseq____"^15logseq____",[242,logseq____"^Qlogseq____",logseq____"Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____",536870923]],[logseq____"^15logseq____",[242,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[242,logseq____"^Flogseq____",266,536870923]],[logseq____"^15logseq____",[242,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[242,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[242,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[242,logseq____"^;logseq____",logseq____"~u65296c01-e42c-4604-9e25-d989d5929b63logseq____",536870923]],[logseq____"^15logseq____",[243,logseq____"^Qlogseq____",logseq____"see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[243,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[243,logseq____"^Flogseq____",249,536870923]],[logseq____"^15logseq____",[243,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[243,logseq____"^Vlogseq____",249,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",211,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",219,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",220,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",226,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[243,logseq____"^Hlogseq____",211,536870923]],[logseq____"^15logseq____",[243,logseq____"^Hlogseq____",216,536870923]],[logseq____"^15logseq____",[243,logseq____"^Hlogseq____",219,536870923]],[logseq____"^15logseq____",[243,logseq____"^Hlogseq____",220,536870923]],[logseq____"^15logseq____",[243,logseq____"^Hlogseq____",226,536870923]],[logseq____"^15logseq____",[243,logseq____"^Hlogseq____",227,536870923]],[logseq____"^15logseq____",[243,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[243,logseq____"^;logseq____",logseq____"~u65296c01-5488-4c77-96f4-8e0a81f0a455logseq____",536870923]],[logseq____"^15logseq____",[244,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 q(u,w))\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Flogseq____",269,536870923]],[logseq____"^15logseq____",[244,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[244,logseq____"^Vlogseq____",269,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[244,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[244,logseq____"^;logseq____",logseq____"~u65296c01-3087-4ea7-a03d-973d6c1250c6logseq____",536870923]],[logseq____"^15logseq____",[245,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____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Flogseq____",259,536870923]],[logseq____"^15logseq____",[245,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[245,logseq____"^Vlogseq____",259,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[245,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[245,logseq____"^;logseq____",logseq____"~u65296c01-f3b0-4497-84f4-23b14ce25f94logseq____",536870923]],[logseq____"^15logseq____",[246,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____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Flogseq____",241,536870923]],[logseq____"^15logseq____",[246,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[246,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[246,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[246,logseq____"^;logseq____",logseq____"~u65296c01-3f31-4b98-929e-17f21cd72d43logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Qlogseq____",logseq____"## [[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Flogseq____",250,536870923]],[logseq____"^15logseq____",[247,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[247,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",210,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[247,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870923]],[logseq____"^15logseq____",[247,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[247,logseq____"^Hlogseq____",210,536870923]],[logseq____"^15logseq____",[247,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[247,logseq____"^;logseq____",logseq____"~u65296c01-1ef9-4e6a-ad58-26f9556d44cflogseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Qlogseq____",logseq____"[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Flogseq____",247,536870923]],[logseq____"^15logseq____",[248,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[248,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[248,logseq____"^Hlogseq____",218,536870923]],[logseq____"^15logseq____",[248,logseq____"^Hlogseq____",222,536870923]],[logseq____"^15logseq____",[248,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[248,logseq____"^;logseq____",logseq____"~u65296c01-d25b-49f2-aa18-baaac2b3adf9logseq____",536870923]],[logseq____"^15logseq____",[249,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____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Flogseq____",273,536870923]],[logseq____"^15logseq____",[249,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[249,logseq____"^Vlogseq____",217,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[249,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[249,logseq____"^;logseq____",logseq____"~u65296c01-f2ae-4339-8f1a-980268c9eb19logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Qlogseq____",logseq____"Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Flogseq____",237,536870923]],[logseq____"^15logseq____",[250,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[250,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[250,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[250,logseq____"^;logseq____",logseq____"~u65296c01-a198-4553-b650-10365f430b07logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Qlogseq____",logseq____"Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Flogseq____",263,536870923]],[logseq____"^15logseq____",[251,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[251,logseq____"^Vlogseq____",247,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",210,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[251,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[251,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[251,logseq____"^;logseq____",logseq____"~u65296c01-1ec8-4db5-9201-d0c828d19945logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Flogseq____",261,536870923]],[logseq____"^15logseq____",[252,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[252,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[252,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[252,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[252,logseq____"^;logseq____",logseq____"~u65296c01-2fd8-4e1e-929a-954debdd5c7dlogseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Qlogseq____",logseq____"see: [[Allquantor]] [[Existenzquantor]]logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Flogseq____",246,536870923]],[logseq____"^15logseq____",[253,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[253,logseq____"^Vlogseq____",246,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",229,536870923]],[logseq____"^15logseq____",[253,logseq____"^Hlogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Hlogseq____",229,536870923]],[logseq____"^15logseq____",[253,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[253,logseq____"^;logseq____",logseq____"~u65296c01-dc69-4ee2-8a08-30fa96daca85logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Qlogseq____",logseq____"# [[Aussageform]]logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Flogseq____",249,536870923]],[logseq____"^15logseq____",[254,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[254,logseq____"^Vlogseq____",217,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[254,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[254,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[254,logseq____"^Hlogseq____",228,536870923]],[logseq____"^15logseq____",[254,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[254,logseq____"^;logseq____",logseq____"~u65296c01-e801-439a-b488-ebebe700a48clogseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Qlogseq____",logseq____"Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Flogseq____",242,536870923]],[logseq____"^15logseq____",[255,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[255,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",214,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",233,536870923]],[logseq____"^15logseq____",[255,logseq____"^Hlogseq____",214,536870923]],[logseq____"^15logseq____",[255,logseq____"^Hlogseq____",233,536870923]],[logseq____"^15logseq____",[255,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[255,logseq____"^;logseq____",logseq____"~u65296c01-a694-47e1-acc3-ac23911ed431logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Qlogseq____",logseq____"[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Flogseq____",254,536870923]],[logseq____"^15logseq____",[256,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[256,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",232,536870923]],[logseq____"^15logseq____",[256,logseq____"^Hlogseq____",228,536870923]],[logseq____"^15logseq____",[256,logseq____"^Hlogseq____",232,536870923]],[logseq____"^15logseq____",[256,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[256,logseq____"^;logseq____",logseq____"~u65296c01-544e-4921-a5bc-d6c2484fd095logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Flogseq____",260,536870923]],[logseq____"^15logseq____",[257,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[257,logseq____"^Vlogseq____",248,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[257,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[257,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[257,logseq____"^;logseq____",logseq____"~u65296c01-4354-4a9d-a7fa-2612a6900e59logseq____",536870923]],[logseq____"^15logseq____",[258,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____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Flogseq____",255,536870923]],[logseq____"^15logseq____",[258,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[258,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[258,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[258,logseq____"^;logseq____",logseq____"~u65296c01-64a8-4e44-b17f-059ffeed7f73logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Flogseq____",262,536870923]],[logseq____"^15logseq____",[259,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[259,logseq____"^Vlogseq____",262,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[259,logseq____"^Hlogseq____",221,536870923]],[logseq____"^15logseq____",[259,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[259,logseq____"^;logseq____",logseq____"~u65296c01-5e1e-4f0c-84f2-bc7c6dc46f42logseq____",536870923]],[logseq____"^15logseq____",[260,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____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Flogseq____",248,536870923]],[logseq____"^15logseq____",[260,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[260,logseq____"^Vlogseq____",248,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[260,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[260,logseq____"^;logseq____",logseq____"~u65296c01-4d53-475e-a843-f31dce40b23flogseq____",536870923]],[logseq____"^15logseq____",[261,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____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Flogseq____",256,536870923]],[logseq____"^15logseq____",[261,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[261,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",170,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",174,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",231,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",170,536870923]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",174,536870923]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",231,536870923]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",234,536870923]],[logseq____"^15logseq____",[261,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[261,logseq____"^;logseq____",logseq____"~u65296c01-e73b-4b7f-872e-fdacad56bea4logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Qlogseq____",logseq____"Betrachte $\\logseq____"xlogseq____<y\\logseq____"$ als AF über $\\\\Reals, \\\\Reals$logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Flogseq____",257,536870923]],[logseq____"^15logseq____",[262,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[262,logseq____"^Vlogseq____",257,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[262,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[262,logseq____"^;logseq____",logseq____"~u65296c01-7a4d-4acf-b578-06c60d4dfe33logseq____",536870923]],[logseq____"^15logseq____",[263,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____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Flogseq____",247,536870923]],[logseq____"^15logseq____",[263,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[263,logseq____"^Vlogseq____",247,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",210,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[263,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[263,logseq____"^;logseq____",logseq____"~u65296c01-908b-4cb2-a748-f3e2452083e3logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Qlogseq____",logseq____"wobei $\\\\pi$ eine \\logseq____"[[Permutation]]\\logseq____" der Zahl $(1,2,\\\\cdots,n)$ istlogseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Flogseq____",260,536870923]],[logseq____"^15logseq____",[264,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[264,logseq____"^Vlogseq____",260,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[264,logseq____"^Hlogseq____",224,536870923]],[logseq____"^15logseq____",[264,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[264,logseq____"^;logseq____",logseq____"~u65296c01-0633-40db-8515-202ee15c9372logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Qlogseq____",logseq____"Wäre $y$ aus $\\\\Reals$ mit $xlogseq____<y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____<y$, Widerspruch. $\\\\blacksquare$logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Flogseq____",240,536870923]],[logseq____"^15logseq____",[265,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[265,logseq____"^Vlogseq____",240,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[265,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[265,logseq____"^;logseq____",logseq____"~u65296c01-eb80-4036-9dc2-51365faa6928logseq____",536870923]],[logseq____"^15logseq____",[266,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____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Flogseq____",252,536870923]],[logseq____"^15logseq____",[266,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[266,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[266,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[266,logseq____"^;logseq____",logseq____"~u65296c01-8ad2-4168-b480-0a8d7ae31e58logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Qlogseq____",logseq____"$\\\\forall x:p(x)$ ist die [Aussage]([[[]Aussagen]]): $\\logseq____"\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____"\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Flogseq____",242,536870923]],[logseq____"^15logseq____",[267,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[267,logseq____"^Vlogseq____",242,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",166,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",235,536870923]],[logseq____"^15logseq____",[267,logseq____"^Hlogseq____",166,536870923]],[logseq____"^15logseq____",[267,logseq____"^Hlogseq____",235,536870923]],[logseq____"^15logseq____",[267,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[267,logseq____"^;logseq____",logseq____"~u65296c01-47aa-4c7e-8eba-e4b947a50ee3logseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Qlogseq____",logseq____"$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, logseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Flogseq____",245,536870923]],[logseq____"^15logseq____",[268,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[268,logseq____"^Vlogseq____",245,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",212,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",215,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[268,logseq____"^Hlogseq____",212,536870923]],[logseq____"^15logseq____",[268,logseq____"^Hlogseq____",215,536870923]],[logseq____"^15logseq____",[268,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[268,logseq____"^;logseq____",logseq____"~u65296c01-a038-4778-b19f-9ec41ca77c62logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Flogseq____",248,536870923]],[logseq____"^15logseq____",[269,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[269,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[269,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[269,logseq____"^;logseq____",logseq____"~u65296c01-b860-4517-845d-ed15666ffe23logseq____",536870923]],[logseq____"^15logseq____",[270,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____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Flogseq____",266,536870923]],[logseq____"^15logseq____",[270,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[270,logseq____"^Vlogseq____",266,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[270,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[270,logseq____"^;logseq____",logseq____"~u65296c01-aec6-4000-b0f0-3260062783b3logseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Qlogseq____",logseq____"Verschiedene [[Quantoren]] dürfen **nicht** vertauscht 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