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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____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",53,536870919]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",53,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u652dd97b-e34e-4727-a4de-dc8c2dc33276logseq____",536870919]],[logseq____"^15logseq____",[55,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____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",82,536870919]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",82,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u652dd97b-47d2-4b8d-8c1d-c3c20d5468a4logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",81,536870919]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",102,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u652dd97b-3848-413e-a4aa-4c621c98e567logseq____",536870919]],[logseq____"^15logseq____",[57,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____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",62,536870919]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",62,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u652dd97b-b240-45d0-9450-efe41cd6eedalogseq____",536870919]],[logseq____"^15logseq____",[58,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____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",87,536870919]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u652dd97b-5ac9-40fe-a482-9b77eabe049elogseq____",536870919]],[logseq____"^15logseq____",[59,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____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",99,536870919]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",99,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u652dd97b-3e45-4af0-b116-a97698224b1elogseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",62,536870919]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[60,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u652dd97b-b429-4565-a2f2-a526686f83f4logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[61,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[61,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",44,536870919]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",false,536870919]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u652dd97b-cf59-4e70-8655-a081e311c32elogseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",64,536870919]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[62,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",31,536870919]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u652dd97b-08aa-4759-b341-949c998e4987logseq____",536870919]],[logseq____"^15logseq____",[63,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____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",57,536870919]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",62,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u652dd97b-1ad7-437e-97ac-70ed7aeeb065logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",61,536870919]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[64,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u652dd97b-b896-463f-aec5-5975f2c51966logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",61,536870919]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",61,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",46,536870919]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",46,536870919]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u652dd97b-8fc7-4f1c-8ff5-846f0413116flogseq____",536870919]],[logseq____"^15logseq____",[66,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____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",97,536870919]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",30,536870919]],[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____"~u652dd97b-80f8-4d66-8d4c-2e2ef9a42428logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\na^nlogseq____&=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____& a,blogseq____>0\\\\\\\\\\na^2b^2logseq____&=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&=a^{nm}\\\\\\\\\\na^0logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",71,536870919]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",71,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u652dd97b-102d-42ae-8f00-3551c59a93f7logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",51,536870919]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",51,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u652dd97b-e09b-4659-beec-6a329c13d277logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c} (a+b)^0logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 \\\\\\\\\\n(a+b)^1logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^2logseq____&logseq____&logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 2 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^3logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 3 logseq____&logseq____& 3 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^4logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 4 logseq____&logseq____& 6 logseq____&logseq____& 4 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^5logseq____&logseq____&logseq____& 1 logseq____&logseq____& 5 logseq____&logseq____& 10 logseq____&logseq____& 10 logseq____&logseq____& 5 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^6logseq____&logseq____& 1 logseq____&logseq____& 6 logseq____&logseq____& 15 logseq____&logseq____& 20 logseq____&logseq____& 15 logseq____&logseq____& 6 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^7logseq____&1 logseq____&logseq____& 7 logseq____&logseq____&21 logseq____&logseq____& 35 logseq____&logseq____& 35 logseq____&logseq____& \\\\cdots\\\\end{array}logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",84,536870919]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u652dd97b-6e53-4ccd-8b2c-41855b46ad1blogseq____",536870919]],[logseq____"^15logseq____",[70,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____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",52,536870919]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",52,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u652dd97b-f066-44fa-959d-da6a81c56469logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",95,536870919]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",95,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[71,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[71,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[71,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u652dd97b-3ecc-4544-b242-0d1f3466f5c2logseq____",536870919]],[logseq____"^15logseq____",[72,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____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",94,536870919]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",94,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u652dd97b-be60-4691-b354-b12ddf3bd133logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",49,536870919]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",95,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",29,536870919]],[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____",29,536870919]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u652dd97b-a95c-4382-aec8-66dcee91ceedlogseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",89,536870919]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",73,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[74,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[74,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",43,536870919]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u652dd97b-4c5e-436e-854b-5cdac487e63dlogseq____",536870919]],[logseq____"^15logseq____",[75,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____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",104,536870919]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",74,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u652dd97b-1ac0-4a73-8e66-759452909ebalogseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",64,536870919]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",64,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",33,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[76,logseq____"^Hlogseq____",33,536870919]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u652dd97b-b3dc-4c7e-b35a-9b07a4eb20eblogseq____",536870919]],[logseq____"^15logseq____",[77,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____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",80,536870919]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",80,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u652dd97b-c31e-48cd-8e86-a3d57a40f637logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",87,536870919]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",84,536870919]],[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____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[78,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[78,logseq____"^Hlogseq____",32,536870919]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u652dd97b-c64c-4dbf-abcd-c3bd415da0b5logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",67,536870919]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",71,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[79,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u652dd97b-ebc9-492c-bfdf-2e48383c7539logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",55,536870919]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",82,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[80,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u652dd97b-8739-4cfa-be8a-5e6c997b6b22logseq____",536870919]],[logseq____"^15logseq____",[81,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____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",102,536870919]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",102,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",35,536870919]],[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____"~u652dd97b-5588-4cf3-9924-2b98ed626d51logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Flogseq____",48,536870919]],[logseq____"^15logseq____",[82,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[82,logseq____"^Vlogseq____",49,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[82,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[82,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[82,logseq____"^Hlogseq____",39,536870919]],[logseq____"^15logseq____",[82,logseq____"^Hlogseq____",45,536870919]],[logseq____"^15logseq____",[82,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u652dd97b-8dae-478f-b358-5cf8fcaaaaa8logseq____",536870919]],[logseq____"^15logseq____",[83,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____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",74,536870919]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",74,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",26,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[83,logseq____"^Hlogseq____",26,536870919]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u652dd97b-68ac-4b93-9c32-e2c1ca01b18alogseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",88,536870919]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",53,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[84,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",28,536870919]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u652dd97b-8687-4159-b9a4-7962ddc1f74clogseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",58,536870919]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[85,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u652dd97b-8cd6-48c3-ae26-0e9aa575fc5clogseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",76,536870919]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",64,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u652dd97b-40b8-4999-83f8-2f7946de4512logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",69,536870919]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u652dd97b-a8f0-4d82-9c39-57ae5793cc78logseq____",536870919]],[logseq____"^15logseq____",[88,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____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",54,536870919]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",53,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u652dd97b-935d-4698-b137-3e5454b646d5logseq____",536870919]],[logseq____"^15logseq____",[89,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____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",73,536870919]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",73,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u652dd97b-921b-4cf0-9880-b21de84363bdlogseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",66,536870919]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u652dd97b-fb93-44fb-87e7-52e557197308logseq____",536870919]],[logseq____"^15logseq____",[91,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____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",79,536870919]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",79,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u652dd97b-3e8c-4a47-88b8-0ac0b4613293logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",98,536870919]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",98,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[92,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u652dd97b-9742-4c9c-9b2e-b32eb4e9b2d3logseq____",536870919]],[logseq____"^15logseq____",[93,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____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",96,536870919]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",60,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u652dd97b-a2c9-4bc6-9388-ebab8673507clogseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",52,536870919]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[94,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[94,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u652dd97b-85ae-4a48-af34-172b352ed037logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",53,536870919]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[95,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[95,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[95,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u652dd97b-b638-401a-9471-83430ed3839flogseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Flogseq____",60,536870919]],[logseq____"^15logseq____",[96,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[96,logseq____"^Vlogseq____",60,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[96,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[96,logseq____"^;logseq____",logseq____"~u652dd97b-6760-4eb6-988a-5e6d61238c8flogseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Qlogseq____",logseq____"# 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1}\\\\quad xlogseq____<3$\\n\\\\begin{align}\\n|x-3|logseq____&=-x+3\\\\\\\\\\n-x+3logseq____&logseq____<5 logseq____&|logseq____&-3\\\\\\\\\\n-xlogseq____&logseq____<2 logseq____&|logseq____&*-1\\\\\\\\\\nxlogseq____&logseq____>-2\\\\\\\\\\nL_1logseq____&=(-2,3)\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[148,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[148,logseq____"^Flogseq____",123,536870920]],[logseq____"^15logseq____",[148,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[148,logseq____"^Vlogseq____",123,536870920]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[148,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[148,logseq____"^;logseq____",logseq____"~u652dd97b-977e-4254-a8e3-df4cb39e62e9logseq____",536870920]],[logseq____"^15logseq____",[149,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1} \\\\quad xlogseq____<-5$\\n\\\\begin{align}\\nx+5logseq____&logseq____<0\\\\\\\\\\n|x+5|logseq____&=-(x+5)=-x-5\\\\\\\\\\nx-3logseq____&logseq____<0\\\\\\\\\\n|x-3|logseq____&=-(x-3)=-x+3\\\\\\\\\\n-x-5logseq____&logseq____< 2(-x+3)\\\\\\\\\\n-x-5logseq____&logseq____<-2x+6 logseq____&|logseq____&+5+2x\\\\\\\\\\nxlogseq____<11\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____<-5,x\\\\le11\\\\right\\\\}=(-\\\\infty,-5)\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[149,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[149,logseq____"^Flogseq____",127,536870920]],[logseq____"^15logseq____",[149,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[149,logseq____"^Vlogseq____",127,536870920]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[149,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[149,logseq____"^;logseq____",logseq____"~u652dd97b-63fc-4f1f-ac48-f8bf0df6e213logseq____",536870920]],[logseq____"^15logseq____",[150,logseq____"^Qlogseq____",logseq____"$\\\\text{Lösungsmenge der Gleichung }x^2+\\\\underbrace{4}_p x-\\\\underbrace{12}_q=0$\\n\\\\begin{align}\\nx_{1,2}logseq____&=\\\\frac{-p}2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\nlogseq____&=-2\\\\pm\\\\sqrt{\\\\frac{16}4-(-12)}\\\\\\\\\\nlogseq____&=-2\\\\pm4\\\\\\\\\\nLlogseq____&=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_\\\\text{Name}\\\\middle|\\\\underbrace{x^2+4x-12=0}_\\\\text{Eigenschaft}\\\\right\\\\}\\\\\\\\\\nLlogseq____&=\\\\left\\\\{2,-6\\\\right\\\\}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[150,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[150,logseq____"^Flogseq____",124,536870920]],[logseq____"^15logseq____",[150,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[150,logseq____"^Vlogseq____",124,536870920]],[logseq____"^15logseq____",[150,logseq____"^Ulogseq____",111,536870920]],[logseq____"^15logseq____",[150,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[150,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[150,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[150,logseq____"^;logseq____",logseq____"~u652dd97b-0827-44d8-95a6-8f58f40d6447logseq____",536870920]],[logseq____"^15logseq____",[151,logseq____"^Qlogseq____",logseq____"Bei Multiplikation oder Division mit einem Betrag einer negativen Zahl nicht Anwendbar, da ein [[Betrag]] immer Positiv istlogseq____",536870920]],[logseq____"^15logseq____",[151,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[151,logseq____"^Flogseq____",161,536870920]],[logseq____"^15logseq____",[151,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[151,logseq____"^Vlogseq____",161,536870920]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",110,536870920]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[151,logseq____"^Hlogseq____",113,536870920]],[logseq____"^15logseq____",[151,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[151,logseq____"^;logseq____",logseq____"~u652dd97b-bb28-4345-aad2-d0831a1b4d2clogseq____",536870920]],[logseq____"^15logseq____",[152,logseq____"^Qlogseq____",logseq____"Der [[Betrag]] ist der zu [[Abstand]] 0\\n\\\\begin{align}\\nf(x)=logseq____&|x|:=logseq____&\\\\begin{cases}\\nxlogseq____&x\\\\ge0\\\\\\\\\\n-xlogseq____&xlogseq____<0\\n\\\\end{cases}\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[152,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[152,logseq____"^Flogseq____",133,536870920]],[logseq____"^15logseq____",[152,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[152,logseq____"^Vlogseq____",133,536870920]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",112,536870920]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[152,logseq____"^Hlogseq____",112,536870920]],[logseq____"^15logseq____",[152,logseq____"^Hlogseq____",113,536870920]],[logseq____"^15logseq____",[152,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[152,logseq____"^;logseq____",logseq____"~u652dd97b-61ac-4a65-ae92-b04df2b282b3logseq____",536870920]],[logseq____"^15logseq____",[153,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&=x-3\\\\\\\\\\nx-3\\\\le|x+2|\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[153,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[153,logseq____"^Flogseq____",145,536870920]],[logseq____"^15logseq____",[153,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[153,logseq____"^Vlogseq____",145,536870920]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[153,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[153,logseq____"^;logseq____",logseq____"~u652dd97b-4061-4a2b-8e5d-4fded0acacd5logseq____",536870920]],[logseq____"^15logseq____",[154,logseq____"^Qlogseq____",logseq____"### [[Beispiele]]logseq____",536870920]],[logseq____"^15logseq____",[154,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[154,logseq____"^Flogseq____",124,536870920]],[logseq____"^15logseq____",[154,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[154,logseq____"^Vlogseq____",134,536870920]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[154,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870920]],[logseq____"^15logseq____",[154,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[154,logseq____"^Hlogseq____",35,536870920]],[logseq____"^15logseq____",[154,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[154,logseq____"^;logseq____",logseq____"~u652dd97b-eff5-4fff-b49b-8ff4397897b4logseq____",536870920]],[logseq____"^15logseq____",[155,logseq____"^Qlogseq____",logseq____"$\\\\{a,b,c\\\\}$logseq____",536870920]],[logseq____"^15logseq____",[155,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[155,logseq____"^Flogseq____",134,536870920]],[logseq____"^15logseq____",[155,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[155,logseq____"^Vlogseq____",134,536870920]],[logseq____"^15logseq____",[155,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[155,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[155,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[155,logseq____"^;logseq____",logseq____"~u652dd97b-386d-4e45-8e3a-396356fc3c7flogseq____",536870920]],[logseq____"^15logseq____",[156,logseq____"^Qlogseq____",logseq____"Menge aller rellen Zahlen zwischen 4 und $\\\\infty$ ohne 4 und $\\\\infty$\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____>4\\\\right\\\\}=:(4,\\\\infty)\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[156,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[156,logseq____"^Flogseq____",138,536870920]],[logseq____"^15logseq____",[156,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[156,logseq____"^Vlogseq____",154,536870920]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[156,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[156,logseq____"^;logseq____",logseq____"~u652dd97b-67f7-43de-95d9-ddf39d686c6dlogseq____",536870920]],[logseq____"^15logseq____",[157,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup L_2=[3,\\\\infty)\\\\cup\\\\left[\\\\frac12,3\\\\right)=\\\\left[\\\\frac12,\\\\infty\\\\right)\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[157,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[157,logseq____"^Flogseq____",137,536870920]],[logseq____"^15logseq____",[157,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[157,logseq____"^Vlogseq____",145,536870920]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[157,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[157,logseq____"^;logseq____",logseq____"~u652dd97b-7781-42fb-aa4c-446eb02773celogseq____",536870920]],[logseq____"^15logseq____",[158,logseq____"^Qlogseq____",logseq____"[Menge]([[Mengen]]) von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]]) die den gleichen [[Abstand]] r ([[Radius]]) zu einem festen [Punkt]([[Punkte]]) ([[Mittelpunkt]])logseq____",536870920]],[logseq____"^15logseq____",[158,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[158,logseq____"^Flogseq____",131,536870920]],[logseq____"^15logseq____",[158,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[158,logseq____"^Vlogseq____",131,536870920]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",106,536870920]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",107,536870920]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",112,536870920]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",116,536870920]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",117,536870920]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[158,logseq____"^Hlogseq____",107,536870920]],[logseq____"^15logseq____",[158,logseq____"^Hlogseq____",109,536870920]],[logseq____"^15logseq____",[158,logseq____"^Hlogseq____",112,536870920]],[logseq____"^15logseq____",[158,logseq____"^Hlogseq____",116,536870920]],[logseq____"^15logseq____",[158,logseq____"^Hlogseq____",117,536870920]],[logseq____"^15logseq____",[158,logseq____"^Hlogseq____",118,536870920]],[logseq____"^15logseq____",[158,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[158,logseq____"^;logseq____",logseq____"~u652dd97b-e0b0-418c-a7c2-55b42def3e9elogseq____",536870920]],[logseq____"^15logseq____",[159,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1a}\\\\quad x\\\\ge -2$\\n\\\\begin{align}\\n|x+2|logseq____&=x+2\\\\\\\\\\nx-3logseq____&\\\\le x+2 logseq____&|logseq____&+3-x\\\\\\\\\\n0logseq____&\\\\le5\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3,x\\\\ge-2,0\\\\le5\\\\right\\\\}=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3\\\\right\\\\}=[3,\\\\infty)\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[159,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[159,logseq____"^Flogseq____",153,536870920]],[logseq____"^15logseq____",[159,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[159,logseq____"^Vlogseq____",145,536870920]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[159,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[159,logseq____"^;logseq____",logseq____"~u652dd97b-b4b7-442c-b5e9-b029aef71c62logseq____",536870920]],[logseq____"^15logseq____",[160,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 3}\\\\quad xlogseq____>3$\\n\\\\begin{align}\\nx+5logseq____&logseq____>0\\\\\\\\\\n|x+5|logseq____&=x+5\\\\\\\\\\nx-3logseq____&\\\\ge0\\\\\\\\\\n|x-3|logseq____&=x-3\\\\\\\\\\nx+5logseq____&logseq____<2(x-3)\\\\\\\\\\nx+5logseq____&logseq____<2x-3 logseq____&|logseq____& -2x-5\\\\\\\\\\n-xlogseq____&logseq____<-11 logseq____&|logseq____& *(-1)\\\\\\\\\\nxlogseq____&logseq____>11\\n\\\\end{align}\\n\\\\begin{align}\\nL_3=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____>3,xlogseq____>11\\\\right\\\\}=(11,\\\\infty)\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[160,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[160,logseq____"^Flogseq____",136,536870920]],[logseq____"^15logseq____",[160,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[160,logseq____"^Vlogseq____",127,536870920]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[160,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[160,logseq____"^;logseq____",logseq____"~u652dd97b-adbc-48bd-b4ab-66d7b7a60758logseq____",536870920]],[logseq____"^15logseq____",[161,logseq____"^Qlogseq____",logseq____"Regeln 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\\\\text{Tantologie}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Flogseq____",193,536870922]],[logseq____"^15logseq____",[187,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[187,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[187,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[187,logseq____"^;logseq____",logseq____"~u652dd97b-d5c6-46d7-88e6-428f1621e98clogseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Flogseq____",210,536870922]],[logseq____"^15logseq____",[188,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[188,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[188,logseq____"^Hlogseq____",35,536870922]],[logseq____"^15logseq____",[188,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[188,logseq____"^;logseq____",logseq____"~u652dd97b-45a4-4aa7-9beb-643616cf4de9logseq____",536870922]],[logseq____"^15logseq____",[189,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____",[189,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Flogseq____",203,536870922]],[logseq____"^15logseq____",[189,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[189,logseq____"^Vlogseq____",203,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[189,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[189,logseq____"^;logseq____",logseq____"~u652dd97b-3ed6-4409-a994-47ce9c09cc94logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Flogseq____",196,536870922]],[logseq____"^15logseq____",[190,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[190,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",174,536870922]],[logseq____"^15logseq____",[190,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[190,logseq____"^;logseq____",logseq____"~u652dd97b-3b30-4902-8027-4024e836cc5alogseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Flogseq____",198,536870922]],[logseq____"^15logseq____",[191,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[191,logseq____"^Vlogseq____",198,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[191,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[191,logseq____"^;logseq____",logseq____"~u652dd97b-1589-4730-92a8-719af23ea7f0logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Qlogseq____",logseq____"### [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Flogseq____",204,536870922]],[logseq____"^15logseq____",[192,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[192,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[192,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[192,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[192,logseq____"^Hlogseq____",182,536870922]],[logseq____"^15logseq____",[192,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[192,logseq____"^;logseq____",logseq____"~u652dd97b-49e0-42e7-a250-f505a5a8d473logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Qlogseq____",logseq____"Weitere [[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Flogseq____",190,536870922]],[logseq____"^15logseq____",[193,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[193,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[193,logseq____"^Hlogseq____",35,536870922]],[logseq____"^15logseq____",[193,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[193,logseq____"^;logseq____",logseq____"~u652dd97b-3fb2-4716-b427-a95406f4b553logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Flogseq____",199,536870922]],[logseq____"^15logseq____",[194,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[194,logseq____"^Vlogseq____",203,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[194,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870922]],[logseq____"^15logseq____",[194,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[194,logseq____"^Hlogseq____",184,536870922]],[logseq____"^15logseq____",[194,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[194,logseq____"^;logseq____",logseq____"~u652dd97b-4135-4486-997e-226aea6df8f5logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Flogseq____",205,536870922]],[logseq____"^15logseq____",[195,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[195,logseq____"^Vlogseq____",208,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",170,536870922]],[logseq____"^15logseq____",[195,logseq____"^Hlogseq____",170,536870922]],[logseq____"^15logseq____",[195,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[195,logseq____"^;logseq____",logseq____"~u652dd97b-1cd1-4f7e-942d-edd3386dd378logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Flogseq____",201,536870922]],[logseq____"^15logseq____",[196,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[196,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",185,536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",178,536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",185,536870922]],[logseq____"^15logseq____",[196,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[196,logseq____"^;logseq____",logseq____"~u652dd97b-b8f5-47b9-9dbe-5c4057b399aelogseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Flogseq____",188,536870922]],[logseq____"^15logseq____",[197,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[197,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",177,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",179,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",183,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[197,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[197,logseq____"^Hlogseq____",177,536870922]],[logseq____"^15logseq____",[197,logseq____"^Hlogseq____",179,536870922]],[logseq____"^15logseq____",[197,logseq____"^Hlogseq____",183,536870922]],[logseq____"^15logseq____",[197,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[197,logseq____"^;logseq____",logseq____"~u652dd97b-6874-4b7d-be2b-6a3115f23ac3logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Qlogseq____",logseq____"### [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Flogseq____",200,536870922]],[logseq____"^15logseq____",[198,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[198,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[198,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],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____"~u652dd97b-3cf0-4591-ad85-23889ee8ee8flogseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&\\logseq____"5\\\\text{ ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Flogseq____",189,536870922]],[logseq____"^15logseq____",[199,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[199,logseq____"^Vlogseq____",203,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[199,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[199,logseq____"^;logseq____",logseq____"~u652dd97b-9c8a-4c72-bbcc-15e0d53b76b5logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Flogseq____",214,536870922]],[logseq____"^15logseq____",[200,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[200,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[200,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[200,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",182,536870922]],[logseq____"^15logseq____",[200,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[200,logseq____"^;logseq____",logseq____"~u652dd97b-1f2c-4652-b9ff-564a1633ecc9logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Flogseq____",198,536870922]],[logseq____"^15logseq____",[201,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[201,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",175,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[201,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[201,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[201,logseq____"^Hlogseq____",175,536870922]],[logseq____"^15logseq____",[201,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[201,logseq____"^;logseq____",logseq____"~u652dd97b-aec4-4a59-93d8-eaab6cf8c8b2logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Flogseq____",200,536870922]],[logseq____"^15logseq____",[202,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[202,logseq____"^Vlogseq____",200,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",171,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",179,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[202,logseq____"^Hlogseq____",171,536870922]],[logseq____"^15logseq____",[202,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[202,logseq____"^Hlogseq____",179,536870922]],[logseq____"^15logseq____",[202,logseq____"^Hlogseq____",186,536870922]],[logseq____"^15logseq____",[202,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[202,logseq____"^;logseq____",logseq____"~u652dd97b-23f5-4107-a3b5-b300f3cfbfb9logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Flogseq____",208,536870922]],[logseq____"^15logseq____",[203,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[203,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[203,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[203,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[203,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[203,logseq____"^;logseq____",logseq____"~u652dd97b-c676-47b4-bade-98284ce52bc0logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Qlogseq____",logseq____"### [[Aussagenlogische Variable]]logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Flogseq____",197,536870922]],[logseq____"^15logseq____",[204,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[204,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",169,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[204,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[204,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[204,logseq____"^Hlogseq____",169,536870922]],[logseq____"^15logseq____",[204,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[204,logseq____"^;logseq____",logseq____"~u652dd97b-2002-49f3-938f-6e74e6b6ea8clogseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Flogseq____",208,536870922]],[logseq____"^15logseq____",[205,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[205,logseq____"^Vlogseq____",208,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",173,536870922]],[logseq____"^15logseq____",[205,logseq____"^Hlogseq____",173,536870922]],[logseq____"^15logseq____",[205,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[205,logseq____"^;logseq____",logseq____"~u652dd97b-f44e-431a-b608-0dfc023287f3logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Flogseq____",202,536870922]],[logseq____"^15logseq____",[206,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[206,logseq____"^Vlogseq____",200,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[206,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[206,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[206,logseq____"^;logseq____",logseq____"~u652dd97b-002c-4d22-a1ed-86bb477804e6logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Flogseq____",201,536870922]],[logseq____"^15logseq____",[207,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[207,logseq____"^Vlogseq____",201,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",175,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[207,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[207,logseq____"^;logseq____",logseq____"~u652dd97b-86b3-4f7f-8587-c1fcd385257dlogseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Flogseq____",165,536870922]],[logseq____"^15logseq____",[208,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[208,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[208,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[208,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[208,logseq____"^17logseq____",false,536870922]],[logseq____"^15logseq____",[208,logseq____"^;logseq____",logseq____"~u652dd97b-522f-4b2b-92d3-792bce03399clogseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Flogseq____",214,536870922]],[logseq____"^15logseq____",[209,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[209,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[209,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[209,logseq____"^Hlogseq____",182,536870922]],[logseq____"^15logseq____",[209,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[209,logseq____"^;logseq____",logseq____"~u652dd97b-cf37-411e-a799-80bf40e30702logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Qlogseq____",logseq____"Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&\\\\quadlogseq____& (\\logseq____"\\\\text{und}\\logseq____")\\\\\\\\\\n(p\\\\lor q) logseq____&logseq____& (\\logseq____"\\\\text{oder}\\logseq____")\\\\\\\\\\n(\\\\neg p) logseq____&logseq____& (\\logseq____"\\\\text{nicht}\\logseq____")\\\\\\\\\\n(p\\\\rightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{impliziert}\\logseq____")\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{genau dann wenn}\\logseq____")\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Flogseq____",194,536870922]],[logseq____"^15logseq____",[210,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[210,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[210,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[210,logseq____"^;logseq____",logseq____"~u652dd97b-1410-4f1b-a8ab-e58651080aedlogseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Qlogseq____",logseq____"[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Flogseq____",204,536870922]],[logseq____"^15logseq____",[211,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[211,logseq____"^Vlogseq____",204,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",169,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[211,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[211,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[211,logseq____"^;logseq____",logseq____"~u652dd97b-fc5f-4b7d-8fc7-9ff6746f82b1logseq____",536870922]],[logseq____"^15logseq____",[212,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____",[212,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Flogseq____",188,536870922]],[logseq____"^15logseq____",[212,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[212,logseq____"^Vlogseq____",188,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[212,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[212,logseq____"^;logseq____",logseq____"~u652dd97b-f9a3-4472-984f-d81af948ef2flogseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Flogseq____",192,536870922]],[logseq____"^15logseq____",[213,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[213,logseq____"^Vlogseq____",192,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",42,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",181,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",42,536870922]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",181,536870922]],[logseq____"^15logseq____",[213,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[213,logseq____"^;logseq____",logseq____"~u652dd97b-88b4-4f4d-93b7-941321a669felogseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der [[Variablen]])logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Flogseq____",192,536870922]],[logseq____"^15logseq____",[214,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[214,logseq____"^Vlogseq____",194,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[214,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[214,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[214,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[214,logseq____"^Hlogseq____",186,536870922]],[logseq____"^15logseq____",[214,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[214,logseq____"^;logseq____",logseq____"~u652dd97b-5f56-4070-992b-3f24a2298705logseq____",536870922]],[logseq____"^15logseq____",[216,logseq____"^Klogseq____",1697503612013,536870923]],[logseq____"^15logseq____",[216,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ylogseq____",logseq____"regelnlogseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^11logseq____",logseq____"Regelnlogseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Blogseq____",1697503612013,536870923]],[logseq____"^15logseq____",[216,logseq____"^;logseq____",logseq____"~u652dd97c-f75a-4b9e-a4e3-ce805ab9ca3blogseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Klogseq____",1697503612000,536870923]],[logseq____"^15logseq____",[217,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ylogseq____",logseq____"de morgansche regelnlogseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^11logseq____",logseq____"de Morgansche 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Aussagen}\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Flogseq____",253,536870923]],[logseq____"^15logseq____",[245,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[245,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[245,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[245,logseq____"^;logseq____",logseq____"~u652dd97b-6c6d-405b-88cf-052443d59f46logseq____",536870923]],[logseq____"^15logseq____",[246,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____",[246,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Flogseq____",276,536870923]],[logseq____"^15logseq____",[246,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[246,logseq____"^Vlogseq____",276,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[246,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[246,logseq____"^;logseq____",logseq____"~u652dd97b-6d26-4df1-9d5a-9cd6f9ddbc56logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Qlogseq____",logseq____"Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Flogseq____",243,536870923]],[logseq____"^15logseq____",[247,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[247,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",220,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",239,536870923]],[logseq____"^15logseq____",[247,logseq____"^Hlogseq____",220,536870923]],[logseq____"^15logseq____",[247,logseq____"^Hlogseq____",239,536870923]],[logseq____"^15logseq____",[247,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[247,logseq____"^;logseq____",logseq____"~u652dd97b-9f68-489c-b605-d5391c66ca56logseq____",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____",276,536870923]],[logseq____"^15logseq____",[248,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[248,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[248,logseq____"^Hlogseq____",224,536870923]],[logseq____"^15logseq____",[248,logseq____"^Hlogseq____",228,536870923]],[logseq____"^15logseq____",[248,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[248,logseq____"^;logseq____",logseq____"~u652dd97b-0b7a-4b95-ba16-4b6bddad021alogseq____",536870923]],[logseq____"^15logseq____",[249,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____",[249,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Flogseq____",277,536870923]],[logseq____"^15logseq____",[249,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[249,logseq____"^Vlogseq____",277,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[249,logseq____"^Hlogseq____",227,536870923]],[logseq____"^15logseq____",[249,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[249,logseq____"^;logseq____",logseq____"~u652dd97b-475a-495b-b399-21fb07cdbf58logseq____",536870923]],[logseq____"^15logseq____",[250,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____",[250,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Flogseq____",247,536870923]],[logseq____"^15logseq____",[250,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[250,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[250,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[250,logseq____"^;logseq____",logseq____"~u652dd97b-8768-4233-a864-aaec97a487aclogseq____",536870923]],[logseq____"^15logseq____",[251,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____",[251,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Flogseq____",245,536870923]],[logseq____"^15logseq____",[251,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[251,logseq____"^Vlogseq____",245,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[251,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[251,logseq____"^;logseq____",logseq____"~u652dd97b-7193-4f93-9c23-e5bdcc1bb7e6logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Qlogseq____",logseq____"Widerspruch = ↯, #logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Flogseq____",266,536870923]],[logseq____"^15logseq____",[252,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[252,logseq____"^Vlogseq____",266,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[252,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[252,logseq____"^;logseq____",logseq____"~u652dd97b-1e50-4e3f-b043-c1cd7d977356logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Flogseq____",273,536870923]],[logseq____"^15logseq____",[253,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[253,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[253,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[253,logseq____"^;logseq____",logseq____"~u652dd97b-6f55-4927-a91e-79f7dee7ab34logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Flogseq____",248,536870923]],[logseq____"^15logseq____",[254,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[254,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[254,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[254,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[254,logseq____"^;logseq____",logseq____"~u652dd97b-bfec-4253-8ba3-602fcbcca397logseq____",536870923]],[logseq____"^15logseq____",[255,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____",[255,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Flogseq____",258,536870923]],[logseq____"^15logseq____",[255,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[255,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[255,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[255,logseq____"^;logseq____",logseq____"~u652dd97b-e8d9-4371-8b20-fdb5a02c7b0blogseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Qlogseq____",logseq____"# [[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Flogseq____",223,536870923]],[logseq____"^15logseq____",[256,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[256,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[256,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[256,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[256,logseq____"^Hlogseq____",216,536870923]],[logseq____"^15logseq____",[256,logseq____"^17logseq____",false,536870923]],[logseq____"^15logseq____",[256,logseq____"^;logseq____",logseq____"~u652dd97b-8d0c-445e-80cc-140cb4884019logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Qlogseq____",logseq____"[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Flogseq____",261,536870923]],[logseq____"^15logseq____",[257,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[257,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",238,536870923]],[logseq____"^15logseq____",[257,logseq____"^Hlogseq____",234,536870923]],[logseq____"^15logseq____",[257,logseq____"^Hlogseq____",238,536870923]],[logseq____"^15logseq____",[257,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[257,logseq____"^;logseq____",logseq____"~u652dd97b-3c22-4323-8984-06f827edbd07logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Qlogseq____",logseq____"Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Flogseq____",250,536870923]],[logseq____"^15logseq____",[258,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[258,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[258,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[258,logseq____"^;logseq____",logseq____"~u652dd97b-7244-4483-9a4a-1e4127c58b9alogseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Flogseq____",263,536870923]],[logseq____"^15logseq____",[259,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[259,logseq____"^Vlogseq____",248,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[259,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[259,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[259,logseq____"^;logseq____",logseq____"~u652dd97b-3082-456f-9607-dd399adeef13logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Qlogseq____",logseq____"Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Flogseq____",278,536870923]],[logseq____"^15logseq____",[260,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[260,logseq____"^Vlogseq____",278,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[260,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[260,logseq____"^;logseq____",logseq____"~u652dd97b-5f14-4ad8-94a7-2c8d01f0b583logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Qlogseq____",logseq____"# [[Aussageform]]logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Flogseq____",275,536870923]],[logseq____"^15logseq____",[261,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[261,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[261,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[261,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",234,536870923]],[logseq____"^15logseq____",[261,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[261,logseq____"^;logseq____",logseq____"~u652dd97b-4961-4497-9953-34acf553ca3clogseq____",536870923]],[logseq____"^15logseq____",[262,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____",[262,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Flogseq____",249,536870923]],[logseq____"^15logseq____",[262,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[262,logseq____"^Vlogseq____",249,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[262,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[262,logseq____"^;logseq____",logseq____"~u652dd97b-d769-4516-ab1b-98dcb2443e32logseq____",536870923]],[logseq____"^15logseq____",[263,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____",[263,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Flogseq____",248,536870923]],[logseq____"^15logseq____",[263,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[263,logseq____"^Vlogseq____",248,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[263,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[263,logseq____"^;logseq____",logseq____"~u652dd97b-0a42-43eb-b0fa-36b4e362cdfblogseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Qlogseq____",logseq____"$\\\\exists x:p(x)$ ist die Aussage: \\logseq____"Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Flogseq____",255,536870923]],[logseq____"^15logseq____",[264,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[264,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",172,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[264,logseq____"^Hlogseq____",172,536870923]],[logseq____"^15logseq____",[264,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[264,logseq____"^;logseq____",logseq____"~u652dd97b-939a-42ae-9a6c-c786452d50c9logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Qlogseq____",logseq____"$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Flogseq____",262,536870923]],[logseq____"^15logseq____",[265,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[265,logseq____"^Vlogseq____",262,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[265,logseq____"^Hlogseq____",218,536870923]],[logseq____"^15logseq____",[265,logseq____"^Hlogseq____",221,536870923]],[logseq____"^15logseq____",[265,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[265,logseq____"^;logseq____",logseq____"~u652dd97b-9601-4cfc-8abb-1accf59a6ff9logseq____",536870923]],[logseq____"^15logseq____",[266,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____",[266,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Flogseq____",274,536870923]],[logseq____"^15logseq____",[266,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[266,logseq____"^Vlogseq____",274,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[266,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[266,logseq____"^;logseq____",logseq____"~u652dd97b-1923-41d4-a502-6d8a1084f15dlogseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Qlogseq____",logseq____"see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Flogseq____",246,536870923]],[logseq____"^15logseq____",[267,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[267,logseq____"^Vlogseq____",246,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",219,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",231,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",236,536870923]],[logseq____"^15logseq____",[267,logseq____"^Hlogseq____",219,536870923]],[logseq____"^15logseq____",[267,logseq____"^Hlogseq____",231,536870923]],[logseq____"^15logseq____",[267,logseq____"^Hlogseq____",236,536870923]],[logseq____"^15logseq____",[267,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[267,logseq____"^;logseq____",logseq____"~u652dd97b-994b-4743-b094-6174d3380d55logseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Qlogseq____",logseq____"wobei $\\\\pi$ eine \\logseq____"[[Permutation]]\\logseq____" der Zahl $(1,2,\\\\cdots,n)$ istlogseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Flogseq____",263,536870923]],[logseq____"^15logseq____",[268,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[268,logseq____"^Vlogseq____",263,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",230,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[268,logseq____"^Hlogseq____",230,536870923]],[logseq____"^15logseq____",[268,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[268,logseq____"^;logseq____",logseq____"~u652dd97b-8b1b-4a2f-a6c7-3e2b21498f88logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Qlogseq____",logseq____"see: [[Allquantor]] [[Existenzquantor]]logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Flogseq____",255,536870923]],[logseq____"^15logseq____",[269,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[269,logseq____"^Vlogseq____",255,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",229,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",235,536870923]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",229,536870923]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",235,536870923]],[logseq____"^15logseq____",[269,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[269,logseq____"^;logseq____",logseq____"~u652dd97b-8f64-4680-8237-0b019991451alogseq____",536870923]],[logseq____"^15logseq____",[270,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____",[270,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Flogseq____",264,536870923]],[logseq____"^15logseq____",[270,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[270,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[270,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[270,logseq____"^;logseq____",logseq____"~u652dd97b-55c6-49e3-a83b-cc13d7636b7blogseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Qlogseq____",logseq____"#FIXMElogseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Flogseq____",270,536870923]],[logseq____"^15logseq____",[271,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[271,logseq____"^Vlogseq____",270,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",42,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[271,logseq____"^Hlogseq____",42,536870923]],[logseq____"^15logseq____",[271,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[271,logseq____"^;logseq____",logseq____"~u652dd97b-088e-47b2-a9a8-7cc309248bf5logseq____",536870923]],[logseq____"^15logseq____",[272,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____",[272,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[272,logseq____"^Flogseq____",243,536870923]],[logseq____"^15logseq____",[272,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[272,logseq____"^Vlogseq____",243,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",172,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",180,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",172,536870923]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",180,536870923]],[logseq____"^15logseq____",[272,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[272,logseq____"^;logseq____",logseq____"~u652dd97b-2d56-43c0-8239-4fed9b7498a2logseq____",536870923]],[logseq____"^15logseq____",[273,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____",[273,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[273,logseq____"^Flogseq____",257,536870923]],[logseq____"^15logseq____",[273,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[273,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",176,536870923]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",180,536870923]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",237,536870923]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",240,536870923]],[logseq____"^15logseq____",[273,logseq____"^Hlogseq____",176,536870923]],[logseq____"^15logseq____",[273,logseq____"^Hlogseq____",180,536870923]],[logseq____"^15logseq____",[273,logseq____"^Hlogseq____",237,536870923]],[logseq____"^15logseq____",[273,logseq____"^Hlogseq____",240,536870923]],[logseq____"^15logseq____",[273,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[273,logseq____"^;logseq____",logseq____"~u652dd97b-e7a5-4668-bf79-90b6f16c6693logseq____",536870923]],[logseq____"^15logseq____",[274,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870923]],[logseq____"^15logseq____",[274,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[274,logseq____"^Flogseq____",249,536870923]],[logseq____"^15logseq____",[274,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[274,logseq____"^Vlogseq____",277,536870923]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",227,536870923]],[logseq____"^15logseq____",[274,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[274,logseq____"^;logseq____",logseq____"~u652dd97b-c26b-42eb-927f-5528f515eae9logseq____",536870923]],[logseq____"^15logseq____",[275,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____",[275,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[275,logseq____"^Flogseq____",256,536870923]],[logseq____"^15logseq____",[275,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[275,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[275,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[275,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[275,logseq____"^;logseq____",logseq____"~u652dd97b-81c0-49b8-9a40-3bd602041c6blogseq____",536870923]],[logseq____"^15logseq____",[276,logseq____"^Qlogseq____",logseq____"## [[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[276,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[276,logseq____"^Flogseq____",270,536870923]],[logseq____"^15logseq____",[276,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[276,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[276,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870923]],[logseq____"^15logseq____",[276,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[276,logseq____"^Hlogseq____",216,536870923]],[logseq____"^15logseq____",[276,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[276,logseq____"^;logseq____",logseq____"~u652dd97b-0a35-491b-84fd-4c6bf2edf2dclogseq____",536870923]],[logseq____"^15logseq____",[277,logseq____"^Qlogseq____",logseq____"Betrachte $\\logseq____"xlogseq____<y\\logseq____"$ als AF über $\\\\Reals, 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