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Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",84,536870919]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[53,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u652decf0-370c-4251-9aec-6a46e2c0f942logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&=a^2-b^2\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",52,536870919]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",52,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u652decf0-9a70-4a1a-8ffc-6335a5131e68logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",71,536870919]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",1],536870919]],[logseq____"^15logseq____",[55,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u652decf0-314f-4cd7-abaf-eeb6672d64dalogseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",94,536870919]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",94,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",26,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",26,536870919]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u652decf0-139e-4f76-a22b-1730ee71f3e1logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",95,536870919]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",82,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[57,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",28,536870919]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u652decf0-fda6-4be9-b620-de092d48005dlogseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",83,536870919]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",83,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u652decf0-fea9-4bca-8c92-f96913e2b387logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",65,536870919]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",68,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u652decf0-9d36-4e0d-b882-5187f4e78658logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&=x^2\\\\\\\\\\ny^2-34y+225logseq____&=0\\\\\\\\\\ny_{1,2}logseq____&=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&\\\\rightarrow logseq____&x_1=5;logseq____&x_2=-5\\\\\\\\\\nx^2=9logseq____&\\\\rightarrow logseq____&x_1=3;logseq____&x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",96,536870919]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",94,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u652decf0-4f94-4914-ba45-583658cf59c3logseq____",536870919]],[logseq____"^15logseq____",[61,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____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",53,536870919]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u652decf0-2f41-4d78-86c1-604520cccc1clogseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",92,536870919]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[62,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[62,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",39,536870919]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",45,536870919]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u652decf0-43f4-4913-a1ad-7a951e966efalogseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",70,536870919]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",70,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u652decf0-6cbe-4813-ac44-47b9b8a855fblogseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",69,536870919]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",71,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u652decf0-9c44-4e85-96a4-99b33a27c944logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",68,536870919]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",68,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",38,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",38,536870919]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u652decf0-daa5-4e7c-8fc0-2cd67e909b51logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",55,536870919]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[66,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[66,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u652decf0-175a-4d52-b444-a0c6bc9ebf12logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",96,536870919]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",96,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u652decf0-a0cc-4f3a-9fe6-937524983103logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",49,536870919]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",57,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[68,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[68,logseq____"^Hlogseq____",32,536870919]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u652decf0-0586-4bdc-87c5-9c4930ba929clogseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",71,536870919]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",71,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u652decf0-e1bd-4ad9-bf87-e70af022e166logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",101,536870919]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[70,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[70,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[70,logseq____"^Hlogseq____",31,536870919]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u652decf0-fc6a-498b-8157-846a712e9310logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",70,536870919]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[71,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[71,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[71,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u652decf0-0397-4587-bcdf-cf47ee056eb9logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",50,536870919]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",66,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u652decf0-f7f1-4fdf-a0f8-865438b18006logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",84,536870919]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",76,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[73,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[73,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[73,logseq____"^Hlogseq____",29,536870919]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u652decf0-0ee9-471c-8738-ca1259b8404dlogseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",93,536870919]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",101,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u652decf0-1c5c-4796-8b9b-c67a8ceea4b5logseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",61,536870919]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u652decf0-95dd-4c4f-b575-a5e148f57f31logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",82,536870919]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[76,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[76,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[76,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[76,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u652decf0-6bd8-43c1-a276-dd0d35155256logseq____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",79,536870919]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",79,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",46,536870919]],[logseq____"^15logseq____",[77,logseq____"^Hlogseq____",46,536870919]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u652decf0-2689-45ba-9a87-9d33f35a01f4logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"https://www.wolframalpha.comlogseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",77,536870919]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",77,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",46,536870919]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u652decf0-1447-4384-9104-7346f93999c5logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",40,536870919]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[79,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[79,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[79,logseq____"^Hlogseq____",44,536870919]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",false,536870919]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u652decf0-22ce-43d5-8def-e19ec28346b5logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",104,536870919]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",75,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[80,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u652decf0-ff01-4b8f-88ec-edca2f25cc37logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nax^2+bx+clogseq____&=0logseq____&|:a\\\\quadlogseq____&a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&= 0\\\\\\\\\\nplogseq____&=\\\\frac ba,logseq____&q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&=0\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",73,536870919]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",73,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[81,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u652decf0-db23-41f7-b823-0b469f7a147flogseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Flogseq____",66,536870919]],[logseq____"^15logseq____",[82,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[82,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[82,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[82,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[82,logseq____"^Hlogseq____",34,536870919]],[logseq____"^15logseq____",[82,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u652decf0-286f-44b1-a9aa-4da62355b114logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",52,536870919]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",86,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u652decf0-84a4-46ce-8ce6-6fa8632b1a2flogseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",86,536870919]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",76,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[84,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u652decf0-127c-464a-b9cf-b7fd18e07808logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"# [[Wurzelgleichung]]logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",73,536870919]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",76,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[85,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[85,logseq____"^Hlogseq____",30,536870919]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u652decf0-2f3f-4e0e-b1e0-ff3ee7bc6b78logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",76,536870919]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",76,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[86,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[86,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u652decf0-70c8-4011-8b33-d381c660c098logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",102,536870919]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",62,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[87,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u652decf0-63f6-4f6b-90cf-bc454e539651logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&, a,b,logseq____>0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",87,536870919]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u652decf0-d3e8-407c-add3-52b15c48f0dflogseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",97,536870919]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",49,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[89,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u652decf0-99e3-4084-8fed-3d092cf8b0b5logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",72,536870919]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",72,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[90,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u652decf0-a052-41ba-b84e-d91b1284f151logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&= p logseq____&, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&=0\\\\\\\\\\nx^2-7x+12logseq____&=0\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",67,536870919]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",67,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u652decf0-a183-4a83-87a9-11dc212e9852logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",75,536870919]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u652decf0-6a4d-4928-b17f-c2eaa90057c0logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",101,536870919]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",101,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",33,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Hlogseq____",33,536870919]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u652decf0-83bc-4d09-b766-9a944c147c12logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",81,536870919]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",73,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[94,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[94,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[94,logseq____"^Hlogseq____",43,536870919]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u652decf0-c453-4fc4-8b43-36a7bdda78b7logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",47,536870919]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",82,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u652decf0-723a-46a3-81c5-8256813c5b6blogseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Qlogseq____",logseq____"[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0 logseq____&logseq____& \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&=-p logseq____&logseq____& 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von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]]) die den gleichen [[Abstand]] r ([[Radius]]) zu einem festen [Punkt]([[Punkte]]) 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aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____<xlogseq____<4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes 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aller rellen Zahlen zwischen 4 und $\\\\infty$ ohne 4 und 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[[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Flogseq____",209,536870922]],[logseq____"^15logseq____",[188,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[188,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[188,logseq____"^Hlogseq____",35,536870922]],[logseq____"^15logseq____",[188,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[188,logseq____"^;logseq____",logseq____"~u652decf1-08fe-4dbc-9d5b-f305d31302b4logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Flogseq____",213,536870922]],[logseq____"^15logseq____",[189,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[189,logseq____"^Vlogseq____",208,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[189,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[189,logseq____"^;logseq____",logseq____"~u652decf1-ec88-4a48-a1b9-679571aec6ablogseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Flogseq____",204,536870922]],[logseq____"^15logseq____",[190,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[190,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",175,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[190,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[190,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",175,536870922]],[logseq____"^15logseq____",[190,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[190,logseq____"^;logseq____",logseq____"~u652decf1-4910-4b78-aaeb-ba2341e7ba9alogseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Flogseq____",197,536870922]],[logseq____"^15logseq____",[191,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[191,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[191,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[191,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[191,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[191,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[191,logseq____"^;logseq____",logseq____"~u652decf1-8dbd-4607-a534-1a2ce188a67blogseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Flogseq____",204,536870922]],[logseq____"^15logseq____",[192,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[192,logseq____"^Vlogseq____",204,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[192,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[192,logseq____"^;logseq____",logseq____"~u652decf1-3697-4bff-9eb4-b2ad20aff03flogseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Flogseq____",190,536870922]],[logseq____"^15logseq____",[193,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[193,logseq____"^Vlogseq____",190,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",175,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[193,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[193,logseq____"^;logseq____",logseq____"~u652decf1-ed84-4063-ac04-7378a38b7524logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Flogseq____",187,536870922]],[logseq____"^15logseq____",[194,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[194,logseq____"^Vlogseq____",187,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",42,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",181,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[194,logseq____"^Hlogseq____",42,536870922]],[logseq____"^15logseq____",[194,logseq____"^Hlogseq____",181,536870922]],[logseq____"^15logseq____",[194,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[194,logseq____"^;logseq____",logseq____"~u652decf1-a798-4bcc-a029-785de66ae925logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Flogseq____",210,536870922]],[logseq____"^15logseq____",[195,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[195,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[195,logseq____"^Hlogseq____",35,536870922]],[logseq____"^15logseq____",[195,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[195,logseq____"^;logseq____",logseq____"~u652decf1-a765-4590-b968-3ad99125621alogseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Qlogseq____",logseq____"### [[Aussagenlogische Variable]]logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Flogseq____",200,536870922]],[logseq____"^15logseq____",[196,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[196,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",169,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[196,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[196,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",169,536870922]],[logseq____"^15logseq____",[196,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[196,logseq____"^;logseq____",logseq____"~u652decf1-a75c-447a-94b2-ac74640b810elogseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Flogseq____",165,536870922]],[logseq____"^15logseq____",[197,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[197,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[197,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[197,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[197,logseq____"^17logseq____",false,536870922]],[logseq____"^15logseq____",[197,logseq____"^;logseq____",logseq____"~u652decf1-1213-4223-98c9-5d7b3319e65dlogseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Qlogseq____",logseq____"Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Flogseq____",191,536870922]],[logseq____"^15logseq____",[198,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[198,logseq____"^Vlogseq____",191,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[198,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[198,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[198,logseq____"^;logseq____",logseq____"~u652decf1-c25d-40d0-bbf1-56eb961d09eblogseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Flogseq____",197,536870922]],[logseq____"^15logseq____",[199,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[199,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",173,536870922]],[logseq____"^15logseq____",[199,logseq____"^Hlogseq____",173,536870922]],[logseq____"^15logseq____",[199,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[199,logseq____"^;logseq____",logseq____"~u652decf1-59bb-4a81-be7b-aa881d1065a2logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Flogseq____",195,536870922]],[logseq____"^15logseq____",[200,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[200,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",177,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",179,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",183,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",177,536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",179,536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",183,536870922]],[logseq____"^15logseq____",[200,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[200,logseq____"^;logseq____",logseq____"~u652decf1-369c-44e1-b39b-f223599d1590logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Qlogseq____",logseq____"[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Flogseq____",196,536870922]],[logseq____"^15logseq____",[201,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[201,logseq____"^Vlogseq____",196,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",169,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[201,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[201,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[201,logseq____"^;logseq____",logseq____"~u652decf1-7ea0-4824-8150-514d236f294blogseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&\\\\rightarrow q logseq____&\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Flogseq____",188,536870922]],[logseq____"^15logseq____",[202,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[202,logseq____"^Vlogseq____",188,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[202,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[202,logseq____"^;logseq____",logseq____"~u652decf1-354f-4465-b467-844fde0779bflogseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Flogseq____",190,536870922]],[logseq____"^15logseq____",[203,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",185,536870922]],[logseq____"^15logseq____",[203,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[203,logseq____"^Hlogseq____",178,536870922]],[logseq____"^15logseq____",[203,logseq____"^Hlogseq____",185,536870922]],[logseq____"^15logseq____",[203,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[203,logseq____"^;logseq____",logseq____"~u652decf1-5ee0-46e5-9a94-e26c4fc7ba5elogseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Qlogseq____",logseq____"### [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Flogseq____",208,536870922]],[logseq____"^15logseq____",[204,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[204,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[204,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[204,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[204,logseq____"^Hlogseq____",174,536870922]],[logseq____"^15logseq____",[204,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[204,logseq____"^;logseq____",logseq____"~u652decf1-15ca-449f-84fc-9640ee0182fflogseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Flogseq____",199,536870922]],[logseq____"^15logseq____",[205,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[205,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",170,536870922]],[logseq____"^15logseq____",[205,logseq____"^Hlogseq____",170,536870922]],[logseq____"^15logseq____",[205,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[205,logseq____"^;logseq____",logseq____"~u652decf1-c3cc-410c-abd9-3614c270ded5logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Flogseq____",211,536870922]],[logseq____"^15logseq____",[206,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[206,logseq____"^Vlogseq____",211,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[206,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[206,logseq____"^Hlogseq____",182,536870922]],[logseq____"^15logseq____",[206,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[206,logseq____"^;logseq____",logseq____"~u652decf1-d43e-4b98-b7a0-9a4b7924577clogseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Flogseq____",195,536870922]],[logseq____"^15logseq____",[207,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[207,logseq____"^Vlogseq____",195,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[207,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[207,logseq____"^;logseq____",logseq____"~u652decf1-2770-4b2f-a80e-22fec8f92750logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Flogseq____",211,536870922]],[logseq____"^15logseq____",[208,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[208,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[208,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[208,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[208,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[208,logseq____"^Hlogseq____",182,536870922]],[logseq____"^15logseq____",[208,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[208,logseq____"^;logseq____",logseq____"~u652decf1-c8c3-4518-89e8-b6291b467739logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Flogseq____",203,536870922]],[logseq____"^15logseq____",[209,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[209,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[209,logseq____"^Hlogseq____",174,536870922]],[logseq____"^15logseq____",[209,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[209,logseq____"^;logseq____",logseq____"~u652decf1-0a8a-4f75-a867-6e4d4cd6b936logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Qlogseq____",logseq____"Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&\\\\quadlogseq____& (\\logseq____"\\\\text{und}\\logseq____")\\\\\\\\\\n(p\\\\lor q) logseq____&logseq____& (\\logseq____"\\\\text{oder}\\logseq____")\\\\\\\\\\n(\\\\neg p) logseq____&logseq____& (\\logseq____"\\\\text{nicht}\\logseq____")\\\\\\\\\\n(p\\\\rightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{impliziert}\\logseq____")\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{genau dann wenn}\\logseq____")\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Flogseq____",214,536870922]],[logseq____"^15logseq____",[210,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[210,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[210,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[210,logseq____"^;logseq____",logseq____"~u652decf1-b24c-4399-a952-6b3e4e64e254logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der [[Variablen]])logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Flogseq____",187,536870922]],[logseq____"^15logseq____",[211,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[211,logseq____"^Vlogseq____",214,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[211,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[211,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[211,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[211,logseq____"^Hlogseq____",186,536870922]],[logseq____"^15logseq____",[211,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[211,logseq____"^;logseq____",logseq____"~u652decf1-272f-46f3-afd8-21706f52e1d4logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&\\logseq____"5\\\\text{ ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Flogseq____",198,536870922]],[logseq____"^15logseq____",[212,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[212,logseq____"^Vlogseq____",191,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[212,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[212,logseq____"^;logseq____",logseq____"~u652decf1-0e4d-44bc-9cc8-3116f62692a8logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Flogseq____",208,536870922]],[logseq____"^15logseq____",[213,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[213,logseq____"^Vlogseq____",208,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",171,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",179,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",171,536870922]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",179,536870922]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",186,536870922]],[logseq____"^15logseq____",[213,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[213,logseq____"^;logseq____",logseq____"~u652decf1-e759-4f74-a7a0-07eb995aaffblogseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Flogseq____",212,536870922]],[logseq____"^15logseq____",[214,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[214,logseq____"^Vlogseq____",191,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[214,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870922]],[logseq____"^15logseq____",[214,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[214,logseq____"^Hlogseq____",184,536870922]],[logseq____"^15logseq____",[214,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[214,logseq____"^;logseq____",logseq____"~u652decf1-c2f9-476a-8d5f-99c973e509belogseq____",536870922]],[logseq____"^15logseq____",[216,logseq____"^Klogseq____",1697508593362,536870923]],[logseq____"^15logseq____",[216,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ylogseq____",logseq____"regelnlogseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^11logseq____",logseq____"Regelnlogseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Blogseq____",1697508593362,536870923]],[logseq____"^15logseq____",[216,logseq____"^;logseq____",logseq____"~u652decf1-1b8a-4cc2-9636-8bbb575ca1a5logseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Klogseq____",1697508593347,536870923]],[logseq____"^15logseq____",[217,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ylogseq____",logseq____"de 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[[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Flogseq____",278,536870923]],[logseq____"^15logseq____",[244,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[244,logseq____"^Vlogseq____",278,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",219,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",231,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",236,536870923]],[logseq____"^15logseq____",[244,logseq____"^Hlogseq____",219,536870923]],[logseq____"^15logseq____",[244,logseq____"^Hlogseq____",231,536870923]],[logseq____"^15logseq____",[244,logseq____"^Hlogseq____",236,536870923]],[logseq____"^15logseq____",[244,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[244,logseq____"^;logseq____",logseq____"~u652decf1-756c-4685-b972-242507cd552clogseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Flogseq____",269,536870923]],[logseq____"^15logseq____",[245,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[245,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[245,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[245,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[245,logseq____"^;logseq____",logseq____"~u652decf1-a4a9-49fc-a082-7a480841d364logseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Qlogseq____",logseq____"Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Flogseq____",276,536870923]],[logseq____"^15logseq____",[246,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[246,logseq____"^Vlogseq____",264,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[246,logseq____"^Hlogseq____",228,536870923]],[logseq____"^15logseq____",[246,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[246,logseq____"^;logseq____",logseq____"~u652decf1-d100-4bc9-8daf-691d9e93726elogseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Qlogseq____",logseq____"Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Flogseq____",273,536870923]],[logseq____"^15logseq____",[247,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[247,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[247,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[247,logseq____"^;logseq____",logseq____"~u652decf1-b252-4609-9a82-b902fbb6f1f2logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Qlogseq____",logseq____"Widerspruch = ↯, #logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Flogseq____",256,536870923]],[logseq____"^15logseq____",[248,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[248,logseq____"^Vlogseq____",256,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[248,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[248,logseq____"^;logseq____",logseq____"~u652decf1-2a6f-43cd-8ed8-61e73c2c62ablogseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Qlogseq____",logseq____"Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über 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[[Existenzquantor]]logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Flogseq____",274,536870923]],[logseq____"^15logseq____",[250,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[250,logseq____"^Vlogseq____",274,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",229,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",235,536870923]],[logseq____"^15logseq____",[250,logseq____"^Hlogseq____",229,536870923]],[logseq____"^15logseq____",[250,logseq____"^Hlogseq____",235,536870923]],[logseq____"^15logseq____",[250,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[250,logseq____"^;logseq____",logseq____"~u652decf1-79be-47e2-b8b2-b1b9e75966f9logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Flogseq____",275,536870923]],[logseq____"^15logseq____",[251,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[251,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[251,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[251,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[251,logseq____"^;logseq____",logseq____"~u652decf1-b432-41e5-9884-28fb4509cba6logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Qlogseq____",logseq____"$\\\\exists x:p(x)$ ist die Aussage: \\logseq____"Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Flogseq____",274,536870923]],[logseq____"^15logseq____",[252,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[252,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",172,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[252,logseq____"^Hlogseq____",172,536870923]],[logseq____"^15logseq____",[252,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[252,logseq____"^;logseq____",logseq____"~u652decf1-0549-4c7b-9a97-58950a65b23alogseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Qlogseq____",logseq____"# [[Aussageform]]logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Flogseq____",241,536870923]],[logseq____"^15logseq____",[253,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[253,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[253,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[253,logseq____"^Hlogseq____",234,536870923]],[logseq____"^15logseq____",[253,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[253,logseq____"^;logseq____",logseq____"~u652decf1-097d-47aa-ab1b-efd0a542ec9clogseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist 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$\\logseq____"xlogseq____<y\\logseq____"$ als AF über $\\\\Reals, \\\\Reals$logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Flogseq____",257,536870923]],[logseq____"^15logseq____",[255,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[255,logseq____"^Vlogseq____",257,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[255,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[255,logseq____"^;logseq____",logseq____"~u652decf1-9304-4e97-8a92-1e458713bb0clogseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Qlogseq____",logseq____"Wäre $y$ aus $\\\\Reals$ mit $xlogseq____<y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____<y$, Widerspruch. $\\\\blacksquare$logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Flogseq____",258,536870923]],[logseq____"^15logseq____",[256,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[256,logseq____"^Vlogseq____",258,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[256,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[256,logseq____"^;logseq____",logseq____"~u652decf1-81af-45b1-bc19-ceb625f45faflogseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Flogseq____",264,536870923]],[logseq____"^15logseq____",[257,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[257,logseq____"^Vlogseq____",275,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[257,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[257,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[257,logseq____"^;logseq____",logseq____"~u652decf1-d256-4cec-8f4f-e75b3ddfe558logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Flogseq____",254,536870923]],[logseq____"^15logseq____",[258,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[258,logseq____"^Vlogseq____",255,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[258,logseq____"^Hlogseq____",227,536870923]],[logseq____"^15logseq____",[258,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[258,logseq____"^;logseq____",logseq____"~u652decf1-076a-4c90-896f-5a7cabaaa5d1logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Qlogseq____",logseq____"Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Flogseq____",270,536870923]],[logseq____"^15logseq____",[259,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[259,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",220,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",239,536870923]],[logseq____"^15logseq____",[259,logseq____"^Hlogseq____",220,536870923]],[logseq____"^15logseq____",[259,logseq____"^Hlogseq____",239,536870923]],[logseq____"^15logseq____",[259,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[259,logseq____"^;logseq____",logseq____"~u652decf1-2b61-4ce6-9305-099b3f088cf7logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Qlogseq____",logseq____"#FIXMElogseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Flogseq____",277,536870923]],[logseq____"^15logseq____",[260,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[260,logseq____"^Vlogseq____",277,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",42,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[260,logseq____"^Hlogseq____",42,536870923]],[logseq____"^15logseq____",[260,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[260,logseq____"^;logseq____",logseq____"~u652decf1-b255-4553-908e-dd313d1c277alogseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Qlogseq____",logseq____"## [[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Flogseq____",277,536870923]],[logseq____"^15logseq____",[261,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[261,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[261,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870923]],[logseq____"^15logseq____",[261,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",216,536870923]],[logseq____"^15logseq____",[261,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[261,logseq____"^;logseq____",logseq____"~u652decf1-b926-47b8-a0a2-a0df24b641f6logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Qlogseq____",logseq____"Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Flogseq____",278,536870923]],[logseq____"^15logseq____",[262,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[262,logseq____"^Vlogseq____",261,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[262,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[262,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[262,logseq____"^;logseq____",logseq____"~u652decf1-5f6d-483d-be2e-5aeca61ba67alogseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Qlogseq____",logseq____"see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Flogseq____",241,536870923]],[logseq____"^15logseq____",[263,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[263,logseq____"^Vlogseq____",241,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",225,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",226,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",232,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",233,536870923]],[logseq____"^15logseq____",[263,logseq____"^Hlogseq____",217,536870923]],[logseq____"^15logseq____",[263,logseq____"^Hlogseq____",222,536870923]],[logseq____"^15logseq____",[263,logseq____"^Hlogseq____",225,536870923]],[logseq____"^15logseq____",[263,logseq____"^Hlogseq____",226,536870923]],[logseq____"^15logseq____",[263,logseq____"^Hlogseq____",232,536870923]],[logseq____"^15logseq____",[263,logseq____"^Hlogseq____",233,536870923]],[logseq____"^15logseq____",[263,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[263,logseq____"^;logseq____",logseq____"~u652decf1-a1b7-4cb2-8478-4a633d4df546logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Flogseq____",275,536870923]],[logseq____"^15logseq____",[264,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[264,logseq____"^Vlogseq____",275,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[264,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[264,logseq____"^;logseq____",logseq____"~u652decf1-23a9-49fa-b0e1-4eb4038e8628logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Flogseq____",251,536870923]],[logseq____"^15logseq____",[265,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[265,logseq____"^Vlogseq____",251,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[265,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[265,logseq____"^;logseq____",logseq____"~u652decf1-581d-4d37-aa01-98350153cd42logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Qlogseq____",logseq____"Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____<x+1=y$ also $xlogseq____<y$. $\\\\blacksquare$logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Flogseq____",254,536870923]],[logseq____"^15logseq____",[266,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[266,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[266,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[266,logseq____"^;logseq____",logseq____"~u652decf1-2268-40df-8576-ac2554d85e97logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Qlogseq____",logseq____"$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Flogseq____",266,536870923]],[logseq____"^15logseq____",[267,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[267,logseq____"^Vlogseq____",266,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[267,logseq____"^Hlogseq____",218,536870923]],[logseq____"^15logseq____",[267,logseq____"^Hlogseq____",221,536870923]],[logseq____"^15logseq____",[267,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[267,logseq____"^;logseq____",logseq____"~u652decf1-893c-4fb5-8288-739d029d9357logseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Qlogseq____",logseq____"[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Flogseq____",253,536870923]],[logseq____"^15logseq____",[268,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[268,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",238,536870923]],[logseq____"^15logseq____",[268,logseq____"^Hlogseq____",234,536870923]],[logseq____"^15logseq____",[268,logseq____"^Hlogseq____",238,536870923]],[logseq____"^15logseq____",[268,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[268,logseq____"^;logseq____",logseq____"~u652decf1-2756-4c87-8208-636da72a6a02logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Qlogseq____",logseq____"[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Flogseq____",268,536870923]],[logseq____"^15logseq____",[269,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[269,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",176,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",180,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",237,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",240,536870923]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",176,536870923]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",180,536870923]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",237,536870923]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",240,536870923]],[logseq____"^15logseq____",[269,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[269,logseq____"^;logseq____",logseq____"~u652decf1-7044-49d3-b2c4-bc71ba06a5c8logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Qlogseq____",logseq____"Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Flogseq____",272,536870923]],[logseq____"^15logseq____",[270,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[270,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[270,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[270,logseq____"^;logseq____",logseq____"~u652decf1-341b-4473-b01a-cf8e2ccc59e6logseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Qlogseq____",logseq____"# [[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Flogseq____",223,536870923]],[logseq____"^15logseq____",[271,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[271,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[271,logseq____"^?logseq____",[logseq____"^ 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