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Dreiecklogseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Blogseq____",1696966758991,536870918]],[logseq____"^15logseq____",[33,logseq____"^;logseq____",logseq____"~u6525a867-83af-42ad-86c8-31f0c38275e1logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Klogseq____",1696966758997,536870918]],[logseq____"^15logseq____",[34,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[34,logseq____"^Ylogseq____",logseq____"rationalmachenlogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^11logseq____",logseq____"Rationalmachenlogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Blogseq____",1696966758997,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u6525a867-8aba-4181-a9d8-88e29334eb50logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Klogseq____",1696966758992,536870918]],[logseq____"^15logseq____",[35,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ylogseq____",logseq____"auffrischung mathe 1logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^11logseq____",logseq____"Auffrischung Mathe 1logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Blogseq____",1696966758992,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u6525a867-a2b2-4858-bb6e-5134a6fff9d1logseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^Klogseq____",1696966759000,536870918]],[logseq____"^15logseq____",[36,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ylogseq____",logseq____"satz von vietalogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^11logseq____",logseq____"Satz von Vietalogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Blogseq____",1696966759000,536870918]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u6525a867-c761-4996-b972-2651584cbfa3logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Klogseq____",1696966758993,536870918]],[logseq____"^15logseq____",[37,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[37,logseq____"^Ylogseq____",logseq____"fixmelogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^11logseq____",logseq____"FIXMElogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Blogseq____",1696966758993,536870918]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u6525a867-d55b-49ef-96e7-01e32ffb2d42logseq____",536870921]],[logseq____"^15logseq____",[38,logseq____"^Klogseq____",1696966758999,536870918]],[logseq____"^15logseq____",[38,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ylogseq____",logseq____"pq-formellogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^11logseq____",logseq____"pq-Formellogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Blogseq____",1696966758999,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u6525a867-d689-41f1-8196-bc1b035ea665logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Klogseq____",1696966758994,536870918]],[logseq____"^15logseq____",[39,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ylogseq____",logseq____"nennerlogseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^11logseq____",logseq____"Nennerlogseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Blogseq____",1696966758994,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u6525a867-6ad3-4356-8be9-1b739bc300b0logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Flogseq____",82,536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",80,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",1],536870918]],[logseq____"^15logseq____",[40,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[40,logseq____"^Hlogseq____",26,536870918]],[logseq____"^15logseq____",[40,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u6525a866-5f5c-41e6-a586-6911861e4e5clogseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Flogseq____",72,536870918]],[logseq____"^15logseq____",[41,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Vlogseq____",72,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",33,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Hlogseq____",33,536870918]],[logseq____"^15logseq____",[41,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u6525a866-ce41-4b8c-b05a-85c7253df7f7logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Flogseq____",59,536870918]],[logseq____"^15logseq____",[42,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^Vlogseq____",40,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[42,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[42,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[42,logseq____"^Hlogseq____",38,536870918]],[logseq____"^15logseq____",[42,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u6525a866-a437-4484-88a2-c012a1ee3c49logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Flogseq____",44,536870918]],[logseq____"^15logseq____",[43,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^Vlogseq____",82,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u6525a866-fb3c-4efd-8f42-3560e4876d8clogseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",82,536870918]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",82,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",37,536870918]],[logseq____"^15logseq____",[44,logseq____"^Hlogseq____",37,536870918]],[logseq____"^15logseq____",[44,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u6525a866-c6df-4569-80b5-5132158e9f25logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Qlogseq____",logseq____"[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0 logseq____&logseq____& \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&=-p logseq____&logseq____& x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",53,536870918]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",42,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[45,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[45,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u6525a866-40a2-4446-af46-f64596ced617logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&, a,b,logseq____>0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",83,536870918]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",64,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",34,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",39,536870918]],[logseq____"^15logseq____",[46,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u6525a866-cb39-49f1-876e-02a6bc05be02logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",78,536870918]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[47,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[47,logseq____"^Hlogseq____",27,536870918]],[logseq____"^15logseq____",[47,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u6525a866-6459-4243-818f-a4109cdc47dalogseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",78,536870918]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",78,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u6525a866-95d9-4c64-b9b9-d6d1d1b602e7logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Qlogseq____",logseq____"![draws/2023-10-08-21-23-31.excalidraw](../assets/excalidraw_svg/2023-10-08-21-23-31.svg)logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",48,536870918]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",78,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u6525a866-2ea9-4842-bff1-c05084bd4c76logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",81,536870918]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",81,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u6525a866-2534-4182-9852-a6bb61624a60logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",47,536870918]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[51,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[51,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u6525a866-84f7-4571-901d-9e2c231cea3alogseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&=a^2-b^2\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",79,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u6525a866-ee3c-46da-829f-d1856fb66df4logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",42,536870918]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",42,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[53,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u6525a866-579d-4651-b57e-ff7d7ae333fblogseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&=a^2+2ab+b^2logseq____&,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&=a^2-2ab+b^2logseq____&,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&=a^2-b^2logseq____&,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",65,536870918]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",65,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u6525a866-5538-4a43-a6d7-8fac3da239a0logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&= \\\\frac1{\\\\ln a}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",58,536870918]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",47,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u6525a866-ff2e-4bec-9dd8-f48f08e69820logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",68,536870918]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",61,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6525a866-f2f4-42a0-9c39-7f2b288e9ffflogseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",76,536870918]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",82,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u6525a866-2831-4a58-81a1-6776bd252b98logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",47,536870918]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",47,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u6525a866-f803-4647-93c5-2afa29de9b30logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nax^2+bx+clogseq____&=0logseq____&|:a\\\\quadlogseq____&a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&= 0\\\\\\\\\\nplogseq____&=\\\\frac ba,logseq____&q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&=0\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",40,536870918]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",40,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u6525a866-2d3f-479b-a45b-e035d6ddb23alogseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",56,536870918]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",56,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",37,536870918]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",37,536870918]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6525a866-512f-4289-833b-42680db06036logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",81,536870918]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[61,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u6525a866-1df4-44a0-afd2-c22337f6ef51logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",84,536870918]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",51,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u6525a866-0262-4af2-8a01-08aebcfd8cd3logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",54,536870918]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",65,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6525a866-d125-480d-b7ed-94d5d288357elogseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",57,536870918]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",82,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",34,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",39,536870918]],[logseq____"^15logseq____",[64,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[64,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",34,536870918]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",39,536870918]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u6525a866-342b-4fb6-8aaf-c15a7a9fcc15logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",61,536870918]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[65,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",30,536870918]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6525a866-b06f-4bbe-915e-f313b936f474logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(2x+y)^4logseq____&=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5logseq____&=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",70,536870918]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",77,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u6525a866-70c1-43e7-b57c-0c08180036e1logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\na^nlogseq____&=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____& a,blogseq____>0\\\\\\\\\\na^2b^2logseq____&=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&=a^{nm}\\\\\\\\\\na^0logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",79,536870918]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",79,536870918]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u6525a866-7f51-4cc8-905a-bd2b3216393dlogseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",61,536870918]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",61,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u6525a866-33bb-4b6d-bb09-21bf89e466d8logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",72,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u6525a866-7c03-4ced-9d35-3d3a0958848alogseq____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c} (a+b)^0logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 \\\\\\\\\\n(a+b)^1logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^2logseq____&logseq____&logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 2 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^3logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 3 logseq____&logseq____& 3 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^4logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 4 logseq____&logseq____& 6 logseq____&logseq____& 4 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^5logseq____&logseq____&logseq____& 1 logseq____&logseq____& 5 logseq____&logseq____& 10 logseq____&logseq____& 10 logseq____&logseq____& 5 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^6logseq____&logseq____& 1 logseq____&logseq____& 6 logseq____&logseq____& 15 logseq____&logseq____& 20 logseq____&logseq____& 15 logseq____&logseq____& 6 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^7logseq____&1 logseq____&logseq____& 7 logseq____&logseq____&21 logseq____&logseq____& 35 logseq____&logseq____& 35 logseq____&logseq____& \\\\cdots\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",77,536870918]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",77,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u6525a866-5b8b-4fc1-a6d7-96b48eabe888logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",73,536870918]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",73,536870918]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u6525a866-5d21-454f-8a6a-f89cbb03920clogseq____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",66,536870918]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",77,536870918]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[72,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[72,logseq____"^Hlogseq____",28,536870918]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u6525a866-929b-482f-abdc-faf9ec1bef1dlogseq____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",79,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u6525a866-92c2-44bf-a02b-9a47d4006f99logseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",76,536870918]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",76,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",37,536870918]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",37,536870918]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u6525a866-8f64-4f71-8610-10cd386cefc3logseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",66,536870918]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",66,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",37,536870918]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",37,536870918]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u6525a866-54ee-4768-a81d-932da8e425d3logseq____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{y^2}=\\\\left|y\\\\right|\\\\\\\\\\n\\\\sqrt[5]{a\\\\sqrt[3]a}=\\\\sqrt[5]{\\\\sqrt[3]{a^3}\\\\sqrt[3]a}\\nlogseq____&=\\\\sqrt[5]{\\\\sqrt[3]{a^4}}\\n=\\\\sqrt[5]{a^\\\\frac43}\\n=a^{\\\\frac43\\\\frac15}=a^\\\\frac4{15}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",43,536870918]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",82,536870918]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u6525a866-549a-4d67-97e2-8a45c4ad86bblogseq____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",63,536870918]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",65,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[77,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[77,logseq____"^Hlogseq____",25,536870918]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u6525a866-a946-44ce-953e-aaae4f964da4logseq____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[78,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[78,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u6525a866-f3b9-41aa-81a1-8981666548eclogseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",80,536870918]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",80,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[79,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[79,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u6525a866-fa35-4315-b2a3-9848d605cd31logseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",65,536870918]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[80,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[80,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[80,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[80,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u6525a866-176d-47e9-ab22-d585affde8cblogseq____",536870918]],[logseq____"^15logseq____",[81,logseq____"^Qlogseq____",logseq____"# Was ist 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Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\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____",536870921]],[logseq____"^15logseq____",[120,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[120,logseq____"^Flogseq____",135,536870921]],[logseq____"^15logseq____",[120,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[120,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",104,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",108,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",115,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[120,logseq____"^Hlogseq____",104,536870921]],[logseq____"^15logseq____",[120,logseq____"^Hlogseq____",108,536870921]],[logseq____"^15logseq____",[120,logseq____"^Hlogseq____",111,536870921]],[logseq____"^15logseq____",[120,logseq____"^Hlogseq____",115,536870921]],[logseq____"^15logseq____",[120,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[120,logseq____"^;logseq____",logseq____"~u6525a867-7e15-4bf1-aa85-9ab90246ec79logseq____",536870921]],[logseq____"^15logseq____",[121,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. 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q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870921]],[logseq____"^15logseq____",[123,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[123,logseq____"^Flogseq____",126,536870921]],[logseq____"^15logseq____",[123,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[123,logseq____"^Vlogseq____",143,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",100,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[123,logseq____"^Hlogseq____",100,536870921]],[logseq____"^15logseq____",[123,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[123,logseq____"^;logseq____",logseq____"~u6525a867-220b-4d1b-959c-d5cefab2d1c6logseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^Flogseq____",121,536870921]],[logseq____"^15logseq____",[124,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[124,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[124,logseq____"^Ulogseq____",102,536870921]],[logseq____"^15logseq____",[124,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[124,logseq____"^Hlogseq____",102,536870921]],[logseq____"^15logseq____",[124,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[124,logseq____"^;logseq____",logseq____"~u6525a867-8e7a-4362-a800-5c7404690217logseq____",536870921]],[logseq____"^15logseq____",[125,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 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[[Tabellenregeln]])logseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Flogseq____",143,536870921]],[logseq____"^15logseq____",[126,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[126,logseq____"^Vlogseq____",143,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",100,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",103,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",104,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",118,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",103,536870921]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",104,536870921]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",111,536870921]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",118,536870921]],[logseq____"^15logseq____",[126,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[126,logseq____"^;logseq____",logseq____"~u6525a867-29ff-4974-90f8-d2516b084800logseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Qlogseq____",logseq____"### [[Tantologie]]logseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Flogseq____",143,536870921]],[logseq____"^15logseq____",[127,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[127,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",106,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[127,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[127,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[127,logseq____"^Hlogseq____",106,536870921]],[logseq____"^15logseq____",[127,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[127,logseq____"^;logseq____",logseq____"~u6525a867-b99d-4e35-ac0e-51fa4abe843clogseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Flogseq____",136,536870921]],[logseq____"^15logseq____",[128,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[128,logseq____"^Vlogseq____",119,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[128,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870921]],[logseq____"^15logseq____",[128,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[128,logseq____"^Hlogseq____",112,536870921]],[logseq____"^15logseq____",[128,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[128,logseq____"^;logseq____",logseq____"~u6525a867-974b-469b-b9eb-6bca55c5d320logseq____",536870921]],[logseq____"^15logseq____",[129,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____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Flogseq____",144,536870921]],[logseq____"^15logseq____",[129,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[129,logseq____"^Vlogseq____",128,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[129,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[129,logseq____"^;logseq____",logseq____"~u6525a867-7bdc-442b-9f66-7684b5e15559logseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Flogseq____",140,536870921]],[logseq____"^15logseq____",[130,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[130,logseq____"^Vlogseq____",140,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[130,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[130,logseq____"^;logseq____",logseq____"~u6525a867-e30b-4d08-a995-56fe54d9a5celogseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Flogseq____",141,536870921]],[logseq____"^15logseq____",[131,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[131,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",106,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[131,logseq____"^Hlogseq____",106,536870921]],[logseq____"^15logseq____",[131,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[131,logseq____"^;logseq____",logseq____"~u6525a867-b638-49e8-af11-6df48f05e166logseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Flogseq____",127,536870921]],[logseq____"^15logseq____",[132,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[132,logseq____"^Vlogseq____",127,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",106,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[132,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[132,logseq____"^;logseq____",logseq____"~u6525a867-03ef-4178-b3d6-afa6354fe88dlogseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Qlogseq____",logseq____"$\\\\text{Weitere Beispiel}$\\n\\\\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____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Flogseq____",131,536870921]],[logseq____"^15logseq____",[133,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[133,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[133,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[133,logseq____"^;logseq____",logseq____"~u6525a867-a8ec-4d58-a51a-b3414909b525logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Flogseq____",129,536870921]],[logseq____"^15logseq____",[134,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[134,logseq____"^Vlogseq____",128,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[134,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870921]],[logseq____"^15logseq____",[134,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[134,logseq____"^Hlogseq____",116,536870921]],[logseq____"^15logseq____",[134,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[134,logseq____"^;logseq____",logseq____"~u6525a867-6db8-4e93-a9e9-3601c945d575logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Flogseq____",125,536870921]],[logseq____"^15logseq____",[135,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[135,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[135,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[135,logseq____"^;logseq____",logseq____"~u6525a867-9be5-43ca-b4a8-d78f15f8a1bblogseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Flogseq____",119,536870921]],[logseq____"^15logseq____",[136,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[136,logseq____"^Vlogseq____",119,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[136,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870921]],[logseq____"^15logseq____",[136,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[136,logseq____"^17logseq____",false,536870921]],[logseq____"^15logseq____",[136,logseq____"^;logseq____",logseq____"~u6525a867-3e82-406e-aa6e-319c6d457064logseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der Variablen)logseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Flogseq____",138,536870921]],[logseq____"^15logseq____",[137,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[137,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",118,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[137,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[137,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[137,logseq____"^Hlogseq____",118,536870921]],[logseq____"^15logseq____",[137,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[137,logseq____"^;logseq____",logseq____"~u6525a867-d7eb-4e86-921a-69e6652b8189logseq____",536870921]],[logseq____"^15logseq____",[138,logseq____"^Qlogseq____",logseq____"### [[Aussageformel]]logseq____",536870921]],[logseq____"^15logseq____",[138,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[138,logseq____"^Flogseq____",145,536870921]],[logseq____"^15logseq____",[138,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[138,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[138,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[138,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[138,logseq____"^Hlogseq____",114,536870921]],[logseq____"^15logseq____",[138,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[138,logseq____"^;logseq____",logseq____"~u6525a867-7849-48fa-a94e-9bb9f5986d48logseq____",536870921]],[logseq____"^15logseq____",[139,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____",536870921]],[logseq____"^15logseq____",[139,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[139,logseq____"^Flogseq____",137,536870921]],[logseq____"^15logseq____",[139,logseq____"^Xlogseq____",119,536870921]],[logseq____"^15logseq____",[139,logseq____"^Vlogseq____",137,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",118,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[139,logseq____"^Hlogseq____",110,536870921]],[logseq____"^15logseq____",[139,logseq____"^Hlogseq____",114,536870921]],[logseq____"^15logseq____",[139,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[139,logseq____"^;logseq____",logseq____"~u6525a867-ebab-4647-aeee-bede6ead9dc6logseq____",536870921]],[logseq____"^15logseq____",[140,logseq____"^Qlogseq____",logseq____"### 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