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62 lines
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Dreiecklogseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Blogseq____",1696962987605,536870918]],[logseq____"^15logseq____",[33,logseq____"^;logseq____",logseq____"~u652599ab-fd74-498b-9fa5-420a51aee424logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Klogseq____",1696962987609,536870918]],[logseq____"^15logseq____",[34,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[34,logseq____"^Ylogseq____",logseq____"rationalmachenlogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^11logseq____",logseq____"Rationalmachenlogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Blogseq____",1696962987609,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u652599ab-481f-414e-9732-22a0d172635blogseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Klogseq____",1696962987606,536870918]],[logseq____"^15logseq____",[35,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ylogseq____",logseq____"auffrischung mathe 1logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^11logseq____",logseq____"Auffrischung Mathe 1logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Blogseq____",1696962987606,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u652599ab-50a0-4618-b417-e6752a22a630logseq____",536870919]],[logseq____"^15logseq____",[36,logseq____"^Klogseq____",1696962987607,536870918]],[logseq____"^15logseq____",[36,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ylogseq____",logseq____"fixmelogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^11logseq____",logseq____"FIXMElogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Blogseq____",1696962987607,536870918]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u652599ac-fd40-4efa-8d66-76d68b5afac0logseq____",536870920]],[logseq____"^15logseq____",[37,logseq____"^Klogseq____",1696962987611,536870918]],[logseq____"^15logseq____",[37,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[37,logseq____"^Ylogseq____",logseq____"pq-formellogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^11logseq____",logseq____"pq-Formellogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Blogseq____",1696962987611,536870918]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u652599ab-0cc3-4366-945b-d716c09a98falogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Klogseq____",1696962987608,536870918]],[logseq____"^15logseq____",[38,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ylogseq____",logseq____"nennerlogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^11logseq____",logseq____"Nennerlogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Blogseq____",1696962987608,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u652599ab-2dec-40ec-a683-7d517ed4e6a7logseq____",536870918]],[logseq____"^15logseq____",[39,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____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Flogseq____",64,536870918]],[logseq____"^15logseq____",[39,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u652599ab-e1ec-400b-84df-a7f94b1b6fedlogseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Flogseq____",50,536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",1],536870918]],[logseq____"^15logseq____",[40,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[40,logseq____"^Hlogseq____",26,536870918]],[logseq____"^15logseq____",[40,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u652599ab-8364-47aa-ae35-7deffb2db5f3logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Flogseq____",44,536870918]],[logseq____"^15logseq____",[41,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[41,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[41,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[41,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u652599ab-41f6-4bcf-b8c9-99bf01077d6dlogseq____",536870918]],[logseq____"^15logseq____",[42,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____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Flogseq____",62,536870918]],[logseq____"^15logseq____",[42,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u652599ab-dedb-4ebd-88a4-42edb66bc1ddlogseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Flogseq____",65,536870918]],[logseq____"^15logseq____",[43,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[43,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[43,logseq____"^Hlogseq____",27,536870918]],[logseq____"^15logseq____",[43,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u652599ab-4ca1-4344-8a6c-4e6081292657logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",58,536870918]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u652599ab-e9f1-4a01-95f0-bda924eda910logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",80,536870918]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[45,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[45,logseq____"^Hlogseq____",30,536870918]],[logseq____"^15logseq____",[45,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u652599ab-0a81-49d6-830a-d20da7293acclogseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",75,536870918]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[46,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[46,logseq____"^Hlogseq____",28,536870918]],[logseq____"^15logseq____",[46,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u652599ab-a037-4773-bcb5-ae99d58e8d9alogseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\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____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u652599ab-1323-4f5d-a243-cfdeab32c375logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",71,536870918]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[48,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[48,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u652599ab-14c0-4c5a-8ef1-c033e0367dfdlogseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&=a^2+2ab+b^2logseq____&,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&=a^2-2ab+b^2logseq____&,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&=a^2-b^2logseq____&,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",45,536870918]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u652599ab-99b7-4e13-a04a-28a3c826a200logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\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____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",39,536870918]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u652599ab-7460-4003-9c01-89af2e5a73c7logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\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____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",66,536870918]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u652599ab-fbe3-4506-8ae2-6af777f3f4a7logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",55,536870918]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u652599ab-f542-4e49-a51e-039c515bf781logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",72,536870918]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[53,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[53,logseq____"^Hlogseq____",25,536870918]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u652599ab-63ca-4eb7-83da-77257f592088logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",77,536870918]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[54,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u652599ab-c87d-4ebd-b0bb-844484b54554logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",48,536870918]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[55,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u652599ab-ff60-43b5-9769-0a7f77a9f6a3logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",47,536870918]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u652599ab-aadf-4f8f-95e4-a62480672803logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",81,536870918]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[57,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u652599ab-c755-419c-8bdd-d5d10aa6daedlogseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",46,536870918]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",33,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",33,536870918]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u652599ab-d5ba-4570-b7e4-0936d3b7d49clogseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",63,536870918]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",37,536870918]],[logseq____"^15logseq____",[59,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[59,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[59,logseq____"^Hlogseq____",37,536870918]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u652599ab-c631-4dd3-a9e7-ea4e11ded155logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",51,536870918]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u652599ab-1646-44bb-8aad-82d9ec4e19d1logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",42,536870918]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u652599ab-0f88-4178-8711-99cf517fb7belogseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",78,536870918]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[62,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[62,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u652599ab-486e-48d2-968e-5d64f16b1afelogseq____",536870918]],[logseq____"^15logseq____",[63,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____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",40,536870918]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u652599ab-089b-45a7-ac4d-5e64aa39de45logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",69,536870918]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",34,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[64,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[64,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",34,536870918]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",38,536870918]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u652599ab-0676-4e5d-bbb2-ddeffb7c66e2logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"![draws/2023-10-08-21-23-31.excalidraw](../assets/excalidraw_svg/2023-10-08-21-23-31.svg)logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",73,536870918]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u652599ab-7316-41e7-8b89-ef5d6ef5e3b5logseq____",536870918]],[logseq____"^15logseq____",[66,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____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u652599ab-76c8-42dc-8992-bb5e557d6d26logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[67,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u652599ab-ffb7-4dea-8268-b6d1f58225e1logseq____",536870918]],[logseq____"^15logseq____",[68,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____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",43,536870918]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u652599ab-c4db-4cd1-a557-791eefbc3bedlogseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",56,536870918]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u652599ab-5fb0-4418-95a8-a41c48886357logseq____",536870918]],[logseq____"^15logseq____",[70,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____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",53,536870918]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u652599ab-1f50-4c04-9b9a-20d93fc10971logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",60,536870918]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u652599ab-be75-43ef-abc9-8d5a4288d3a0logseq____",536870918]],[logseq____"^15logseq____",[72,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____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",49,536870918]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u652599ab-1d1e-4f3f-8ea8-b9c744575968logseq____",536870918]],[logseq____"^15logseq____",[73,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____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u652599ab-d747-4524-aee5-9b28a66dbac7logseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\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____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",70,536870918]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u652599ab-4b20-4125-8722-0333f70f2c6flogseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",74,536870918]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u652599ab-068e-4168-a85f-6595cd792705logseq____",536870918]],[logseq____"^15logseq____",[76,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____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",57,536870918]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u652599ab-456a-4a22-9c35-899ebb945470logseq____",536870918]],[logseq____"^15logseq____",[77,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____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",76,536870918]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u652599ab-d404-44a5-8a8c-99bcb9b2e0b2logseq____",536870918]],[logseq____"^15logseq____",[78,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____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",54,536870918]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u652599ab-746c-4f66-878a-a43f3be9ad54logseq____",536870918]],[logseq____"^15logseq____",[79,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____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",59,536870918]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u652599ab-1bde-4e32-b83f-9269b236e10dlogseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",61,536870918]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[80,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u652599ab-9398-47bd-b8da-02d6dfdde9eblogseq____",536870918]],[logseq____"^15logseq____",[81,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____",536870918]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",68,536870918]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[81,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u652599ab-0e49-464e-9813-1acf299be909logseq____",536870918]],[logseq____"^15logseq____",[83,logseq____"^Klogseq____",1696962987811,536870919]],[logseq____"^15logseq____",[83,logseq____"^@logseq____",false,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ylogseq____",logseq____"auffrischung mathelogseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^11logseq____",logseq____"Auffrischung Mathelogseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Blogseq____",1696962987811,536870919]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u652599ac-1058-4e8b-b41f-883fb7898be8logseq____",536870926]],[logseq____"^15logseq____",[84,logseq____"^Klogseq____",1696962987812,536870919]],[logseq____"^15logseq____",[84,logseq____"^@logseq____",false,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ylogseq____",logseq____"auffrischung mathe 2logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^11logseq____",logseq____"Auffrischung Mathe 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[[Aussagen]]logseq____",536870920]],[logseq____"^15logseq____",[111,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[111,logseq____"^Flogseq____",121,536870920]],[logseq____"^15logseq____",[111,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[111,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",102,536870920]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[111,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[111,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[111,logseq____"^Hlogseq____",102,536870920]],[logseq____"^15logseq____",[111,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[111,logseq____"^;logseq____",logseq____"~u652599ab-9f4e-4bba-ab75-837fb30c3158logseq____",536870920]],[logseq____"^15logseq____",[112,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____",536870920]],[logseq____"^15logseq____",[112,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[112,logseq____"^Flogseq____",119,536870920]],[logseq____"^15logseq____",[112,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[112,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",102,536870920]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[112,logseq____"^Hlogseq____",102,536870920]],[logseq____"^15logseq____",[112,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[112,logseq____"^;logseq____",logseq____"~u652599ab-9d50-4b35-9961-92490dadb4ealogseq____",536870920]],[logseq____"^15logseq____",[113,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\logseq____"5\\\\text{ ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\n\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\\\\\\\n(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\notag\\\\\\\\\\n\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\n\\\\text{ hat eine Lösung }x,y,z\\\\notag\\n\\\\\\\\\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nx^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nx,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\n\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\n\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\n\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[113,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[113,logseq____"^Flogseq____",114,536870920]],[logseq____"^15logseq____",[113,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[113,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[113,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[113,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[113,logseq____"^;logseq____",logseq____"~u652599ab-6ea1-407e-95a3-1c9bba64c880logseq____",536870920]],[logseq____"^15logseq____",[114,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____",536870920]],[logseq____"^15logseq____",[114,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[114,logseq____"^Flogseq____",111,536870920]],[logseq____"^15logseq____",[114,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[114,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",94,536870920]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[114,logseq____"^Hlogseq____",94,536870920]],[logseq____"^15logseq____",[114,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[114,logseq____"^;logseq____",logseq____"~u652599ab-79a7-4151-aa3a-705eab11355dlogseq____",536870920]],[logseq____"^15logseq____",[115,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$|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870920]],[logseq____"^15logseq____",[115,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[115,logseq____"^Flogseq____",122,536870920]],[logseq____"^15logseq____",[115,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[115,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",90,536870920]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[115,logseq____"^Hlogseq____",90,536870920]],[logseq____"^15logseq____",[115,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[115,logseq____"^;logseq____",logseq____"~u652599ab-7cd5-440e-bf02-49d6901ff68clogseq____",536870920]],[logseq____"^15logseq____",[116,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[116,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[116,logseq____"^Flogseq____",112,536870920]],[logseq____"^15logseq____",[116,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[116,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[116,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[116,logseq____"^;logseq____",logseq____"~u652599ab-4516-49af-a887-5ad0c9274cd4logseq____",536870920]],[logseq____"^15logseq____",[117,logseq____"^Qlogseq____",logseq____"[[Aussageformel]]: Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870920]],[logseq____"^15logseq____",[117,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[117,logseq____"^Flogseq____",118,536870920]],[logseq____"^15logseq____",[117,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[117,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",103,536870920]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",104,536870920]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[117,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[117,logseq____"^Hlogseq____",103,536870920]],[logseq____"^15logseq____",[117,logseq____"^Hlogseq____",104,536870920]],[logseq____"^15logseq____",[117,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[117,logseq____"^;logseq____",logseq____"~u652599ab-0235-4527-8c23-93cb6fc6232blogseq____",536870920]],[logseq____"^15logseq____",[118,logseq____"^Qlogseq____",logseq____"[[Aussagenlogische variable]]: [[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____",536870920]],[logseq____"^15logseq____",[118,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[118,logseq____"^Flogseq____",126,536870920]],[logseq____"^15logseq____",[118,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[118,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[118,logseq____"^Ulogseq____",91,536870920]],[logseq____"^15logseq____",[118,logseq____"^Ulogseq____",100,536870920]],[logseq____"^15logseq____",[118,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[118,logseq____"^Hlogseq____",91,536870920]],[logseq____"^15logseq____",[118,logseq____"^Hlogseq____",100,536870920]],[logseq____"^15logseq____",[118,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[118,logseq____"^;logseq____",logseq____"~u652599ab-18ce-43b7-9458-0afd44ddc7a3logseq____",536870920]],[logseq____"^15logseq____",[119,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870920]],[logseq____"^15logseq____",[119,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[119,logseq____"^Flogseq____",113,536870920]],[logseq____"^15logseq____",[119,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[119,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",106,536870920]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[119,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[119,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[119,logseq____"^Hlogseq____",106,536870920]],[logseq____"^15logseq____",[119,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[119,logseq____"^;logseq____",logseq____"~u652599ab-a3b3-43bc-9c1f-7659e7b2ec0clogseq____",536870920]],[logseq____"^15logseq____",[120,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870920]],[logseq____"^15logseq____",[120,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[120,logseq____"^Flogseq____",123,536870920]],[logseq____"^15logseq____",[120,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[120,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",96,536870920]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[120,logseq____"^Hlogseq____",96,536870920]],[logseq____"^15logseq____",[120,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[120,logseq____"^;logseq____",logseq____"~u652599ab-8e33-4647-adc2-025546bb1c96logseq____",536870920]],[logseq____"^15logseq____",[121,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870920]],[logseq____"^15logseq____",[121,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[121,logseq____"^Flogseq____",124,536870920]],[logseq____"^15logseq____",[121,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[121,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",92,536870920]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[121,logseq____"^Hlogseq____",92,536870920]],[logseq____"^15logseq____",[121,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[121,logseq____"^;logseq____",logseq____"~u652599ab-9dbc-496d-b3d3-e1f3dc3d06b2logseq____",536870920]],[logseq____"^15logseq____",[122,logseq____"^Qlogseq____",logseq____"[[Wahrheitswerteverlauf]] einer [[Aussageformel]]: Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870920]],[logseq____"^15logseq____",[122,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[122,logseq____"^Flogseq____",130,536870920]],[logseq____"^15logseq____",[122,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[122,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",90,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",93,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",94,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",101,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",104,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",90,536870920]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",93,536870920]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",94,536870920]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",101,536870920]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",104,536870920]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",108,536870920]],[logseq____"^15logseq____",[122,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[122,logseq____"^;logseq____",logseq____"~u652599ab-8d2c-44b4-8926-f6d931549a88logseq____",536870920]],[logseq____"^15logseq____",[123,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870920]],[logseq____"^15logseq____",[123,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[123,logseq____"^Flogseq____",127,536870920]],[logseq____"^15logseq____",[123,logseq____"^Xlogseq____",109,536870920]],[logseq____"^15logseq____",[123,logseq____"^Vlogseq____",109,536870920]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",90,536870920]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",99,536870920]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",107,536870920]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[123,logseq____"^Hlogseq____",90,536870920]],[logseq____"^15logseq____",[123,logseq____"^Hlogseq____",99,536870920]],[logseq____"^15logseq____",[123,logseq____"^Hlogseq____",107,536870920]],[logseq____"^15logseq____",[123,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[123,logseq____"^;logseq____",logseq____"~u652599ab-6c05-4646-892f-fec942ca49e2logseq____",536870920]],[logseq____"^15logseq____",[124,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. 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Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow 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