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3logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[34,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u65251170-5d17-450a-97f8-11469e9b23ddlogseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Flogseq____",62,536870918]],[logseq____"^15logseq____",[35,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",2],536870918]],[logseq____"^15logseq____",[35,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[35,logseq____"^Hlogseq____",26,536870918]],[logseq____"^15logseq____",[35,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u65251170-db96-4ea7-974b-925c68dc14bdlogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Flogseq____",34,536870918]],[logseq____"^15logseq____",[36,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[36,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[36,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[36,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u65251170-6b59-457b-aaa9-571bf2488367logseq____",536870918]],[logseq____"^15logseq____",[37,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____",[37,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Flogseq____",47,536870918]],[logseq____"^15logseq____",[37,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u65251170-1d71-417f-9615-bc4f6afd5e70logseq____",536870918]],[logseq____"^15logseq____",[38,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____",[38,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Flogseq____",42,536870918]],[logseq____"^15logseq____",[38,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u65251170-aa41-44d1-94cd-15f7892b5cd3logseq____",536870918]],[logseq____"^15logseq____",[39,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____",[39,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Flogseq____",60,536870918]],[logseq____"^15logseq____",[39,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u65251170-3cb0-4cc8-91b5-a72c6ad6187elogseq____",536870918]],[logseq____"^15logseq____",[40,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}\\\\notag\\\\\\\\\\nlogseq____&=\\\\left|y\\\\right|\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u65251170-afb2-4b4c-8ab9-070e00bd4ee9logseq____",536870918]],[logseq____"^15logseq____",[41,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____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Flogseq____",38,536870918]],[logseq____"^15logseq____",[41,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u65251170-4808-43bf-85a2-5527b52c8c41logseq____",536870918]],[logseq____"^15logseq____",[42,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____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Flogseq____",64,536870918]],[logseq____"^15logseq____",[42,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u65251170-4a74-4678-91ea-86e384974266logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Flogseq____",63,536870918]],[logseq____"^15logseq____",[43,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[43,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[43,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u65251170-08d2-4fa1-8254-19af936674b1logseq____",536870918]],[logseq____"^15logseq____",[44,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____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",55,536870918]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u65251170-c316-4ae4-84b0-bb10bc894caalogseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[45,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[45,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[45,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u65251170-8bfe-46ea-aa19-384d14ae598clogseq____",536870918]],[logseq____"^15logseq____",[46,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____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",51,536870918]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u65251170-415d-483e-b8ff-79b272dcd4fdlogseq____",536870918]],[logseq____"^15logseq____",[47,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____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u65251170-e1c0-4e12-8b43-3cf0d35f80f1logseq____",536870918]],[logseq____"^15logseq____",[48,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____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",56,536870918]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u65251170-fa6c-45a5-8c60-e0c957fc8b08logseq____",536870918]],[logseq____"^15logseq____",[49,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____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",57,536870918]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u65251170-02e4-42a4-950b-0e1167f4dbe4logseq____",536870918]],[logseq____"^15logseq____",[50,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____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",44,536870918]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u65251170-b56e-4e57-b451-8b297c007437logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^Hlogseq____",30,536870918]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u65251170-f6a5-4176-88fa-9f339e36943clogseq____",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____",33,536870918]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u65251170-c82e-4109-9fad-6b5593220442logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",49,536870918]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[53,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u65251170-93a5-4efb-a170-f433a0eda341logseq____",536870918]],[logseq____"^15logseq____",[54,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____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",53,536870918]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u65251170-3f6d-41e0-8863-744c05cfb702logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",48,536870918]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[55,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[55,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u65251170-a2a5-4788-9384-c83a08e3ce92logseq____",536870918]],[logseq____"^15logseq____",[56,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____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",61,536870918]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u65251170-eb10-4ca0-a8ac-7f690c47e86flogseq____",536870918]],[logseq____"^15logseq____",[57,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____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",58,536870918]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u65251170-4a1a-4368-aaf8-d80963230586logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",37,536870918]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[58,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u65251170-11b6-4648-8028-20088f5a4b01logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",65,536870918]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u65251170-a6dc-4fec-b8e1-526de7ec4872logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",54,536870918]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[60,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",28,536870918]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u65251170-273d-4032-af55-ca3bf7e7bea3logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",43,536870918]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[61,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",27,536870918]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u65251170-97fa-478d-a35e-cbdd99574ef2logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",50,536870918]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u65251170-d548-49a0-b95b-674faa6ef851logseq____",536870918]],[logseq____"^15logseq____",[63,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____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",39,536870918]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u65251170-f260-4beb-ad79-bdba436d6bb7logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",46,536870918]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[64,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u65251170-b8c0-44a8-ab64-00deb0e0cebdlogseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\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____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",45,536870918]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u65251170-9caf-4894-85e6-21b6dd8dd717logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn 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q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&\\\\rightarrow q logseq____&\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[97,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[97,logseq____"^Flogseq____",112,536870920]],[logseq____"^15logseq____",[97,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[97,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[97,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[97,logseq____"^;logseq____",logseq____"~u65251170-add2-4ea2-9999-05f4e2fe878clogseq____",536870920]],[logseq____"^15logseq____",[98,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____",[98,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[98,logseq____"^Flogseq____",108,536870920]],[logseq____"^15logseq____",[98,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[98,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",80,536870920]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[98,logseq____"^Hlogseq____",80,536870920]],[logseq____"^15logseq____",[98,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[98,logseq____"^;logseq____",logseq____"~u65251170-b8f5-4d1c-8db2-bd8273fdfdbclogseq____",536870920]],[logseq____"^15logseq____",[99,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870920]],[logseq____"^15logseq____",[99,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[99,logseq____"^Flogseq____",113,536870920]],[logseq____"^15logseq____",[99,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[99,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",93,536870920]],[logseq____"^15logseq____",[99,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[99,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[99,logseq____"^Hlogseq____",93,536870920]],[logseq____"^15logseq____",[99,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[99,logseq____"^;logseq____",logseq____"~u65251170-dbeb-4f62-8f40-102adf948870logseq____",536870920]],[logseq____"^15logseq____",[100,logseq____"^Qlogseq____",logseq____"[[Aussagenlogische variable]]: [[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____",536870920]],[logseq____"^15logseq____",[100,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[100,logseq____"^Flogseq____",110,536870920]],[logseq____"^15logseq____",[100,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[100,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",77,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",86,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[100,logseq____"^Hlogseq____",77,536870920]],[logseq____"^15logseq____",[100,logseq____"^Hlogseq____",86,536870920]],[logseq____"^15logseq____",[100,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[100,logseq____"^;logseq____",logseq____"~u65251170-72f1-4f3c-b829-62a19afc6113logseq____",536870920]],[logseq____"^15logseq____",[101,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870920]],[logseq____"^15logseq____",[101,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[101,logseq____"^Flogseq____",102,536870920]],[logseq____"^15logseq____",[101,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[101,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[101,logseq____"^Ulogseq____",81,536870920]],[logseq____"^15logseq____",[101,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[101,logseq____"^Hlogseq____",81,536870920]],[logseq____"^15logseq____",[101,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[101,logseq____"^;logseq____",logseq____"~u65251170-a595-40f2-8633-a6c83fc6b49blogseq____",536870920]],[logseq____"^15logseq____",[102,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870920]],[logseq____"^15logseq____",[102,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[102,logseq____"^Flogseq____",89,536870920]],[logseq____"^15logseq____",[102,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[102,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[102,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[102,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[102,logseq____"^17logseq____",false,536870920]],[logseq____"^15logseq____",[102,logseq____"^;logseq____",logseq____"~u65251170-8907-45f6-b251-af401663d530logseq____",536870920]],[logseq____"^15logseq____",[103,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____",[103,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[103,logseq____"^Flogseq____",106,536870920]],[logseq____"^15logseq____",[103,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[103,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[103,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[103,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[103,logseq____"^;logseq____",logseq____"~u65251170-dc6e-4195-889b-b6a81c593a99logseq____",536870920]],[logseq____"^15logseq____",[104,logseq____"^Qlogseq____",logseq____"[[Kontradiktion]]: Formel, die konstant $f$ istlogseq____",536870920]],[logseq____"^15logseq____",[104,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[104,logseq____"^Flogseq____",114,536870920]],[logseq____"^15logseq____",[104,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[104,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",83,536870920]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[104,logseq____"^Hlogseq____",83,536870920]],[logseq____"^15logseq____",[104,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[104,logseq____"^;logseq____",logseq____"~u65251170-d227-44ff-bf43-20599f5b9257logseq____",536870920]],[logseq____"^15logseq____",[105,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870920]],[logseq____"^15logseq____",[105,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[105,logseq____"^Flogseq____",101,536870920]],[logseq____"^15logseq____",[105,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[105,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",78,536870920]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[105,logseq____"^Hlogseq____",78,536870920]],[logseq____"^15logseq____",[105,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[105,logseq____"^;logseq____",logseq____"~u65251170-3191-4ac6-8560-eeb5c97cf7c0logseq____",536870920]],[logseq____"^15logseq____",[106,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____",[106,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[106,logseq____"^Flogseq____",99,536870920]],[logseq____"^15logseq____",[106,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[106,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[106,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[106,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[106,logseq____"^;logseq____",logseq____"~u65251170-03c8-4207-b79b-48bd33ee7b4alogseq____",536870920]],[logseq____"^15logseq____",[107,logseq____"^Qlogseq____",logseq____"[[Wahrheitswerteverlauf]] einer [[Aussageformel]]: Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870920]],[logseq____"^15logseq____",[107,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[107,logseq____"^Flogseq____",111,536870920]],[logseq____"^15logseq____",[107,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[107,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",76,536870920]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",79,536870920]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",80,536870920]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",87,536870920]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",91,536870920]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",95,536870920]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",76,536870920]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",79,536870920]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",80,536870920]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",87,536870920]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",91,536870920]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",95,536870920]],[logseq____"^15logseq____",[107,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[107,logseq____"^;logseq____",logseq____"~u65251170-b2d8-48b8-9147-a30ff8f3d2aelogseq____",536870920]],[logseq____"^15logseq____",[108,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870920]],[logseq____"^15logseq____",[108,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[108,logseq____"^Flogseq____",105,536870920]],[logseq____"^15logseq____",[108,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[108,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",88,536870920]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[108,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[108,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[108,logseq____"^Hlogseq____",88,536870920]],[logseq____"^15logseq____",[108,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[108,logseq____"^;logseq____",logseq____"~u65251170-1c72-4ffa-9518-fb97c83d3edalogseq____",536870920]],[logseq____"^15logseq____",[109,logseq____"^Qlogseq____",logseq____"logseq____",536870920]],[logseq____"^15logseq____",[109,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[109,logseq____"^Flogseq____",97,536870920]],[logseq____"^15logseq____",[109,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[109,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[109,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[109,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[109,logseq____"^;logseq____",logseq____"~u65251170-226a-46fd-9021-a994e7c62c0blogseq____",536870920]],[logseq____"^15logseq____",[110,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", jetzt die [[Semantik]]. Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\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____",536870920]],[logseq____"^15logseq____",[110,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[110,logseq____"^Flogseq____",103,536870920]],[logseq____"^15logseq____",[110,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[110,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[110,logseq____"^Ulogseq____",80,536870920]],[logseq____"^15logseq____",[110,logseq____"^Ulogseq____",84,536870920]],[logseq____"^15logseq____",[110,logseq____"^Ulogseq____",87,536870920]],[logseq____"^15logseq____",[110,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[110,logseq____"^Ulogseq____",92,536870920]],[logseq____"^15logseq____",[110,logseq____"^Hlogseq____",80,536870920]],[logseq____"^15logseq____",[110,logseq____"^Hlogseq____",84,536870920]],[logseq____"^15logseq____",[110,logseq____"^Hlogseq____",87,536870920]],[logseq____"^15logseq____",[110,logseq____"^Hlogseq____",92,536870920]],[logseq____"^15logseq____",[110,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[110,logseq____"^;logseq____",logseq____"~u65251170-2761-4036-9070-811a4583e051logseq____",536870920]],[logseq____"^15logseq____",[111,logseq____"^Qlogseq____",logseq____"[[Belegung]] (der Variablen): Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____",536870920]],[logseq____"^15logseq____",[111,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[111,logseq____"^Flogseq____",115,536870920]],[logseq____"^15logseq____",[111,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[111,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",86,536870920]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",91,536870920]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",95,536870920]],[logseq____"^15logseq____",[111,logseq____"^Hlogseq____",86,536870920]],[logseq____"^15logseq____",[111,logseq____"^Hlogseq____",91,536870920]],[logseq____"^15logseq____",[111,logseq____"^Hlogseq____",95,536870920]],[logseq____"^15logseq____",[111,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[111,logseq____"^;logseq____",logseq____"~u65251170-ce0c-4a8b-b6d3-f273fcf60baelogseq____",536870920]],[logseq____"^15logseq____",[112,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870920]],[logseq____"^15logseq____",[112,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[112,logseq____"^Flogseq____",116,536870920]],[logseq____"^15logseq____",[112,logseq____"^Xlogseq____",89,536870920]],[logseq____"^15logseq____",[112,logseq____"^Vlogseq____",89,536870920]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",82,536870920]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",89,536870920]],[logseq____"^15logseq____",[112,logseq____"^Hlogseq____",82,536870920]],[logseq____"^15logseq____",[112,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[112,logseq____"^;logseq____",logseq____"~u65251170-a9eb-4f94-a14a-24670c643614logseq____",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 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