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62 lines
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Dreiecklogseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Blogseq____",1696965254589,536870918]],[logseq____"^15logseq____",[33,logseq____"^;logseq____",logseq____"~u6525a286-67d7-49c7-96d6-831969360a7blogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Klogseq____",1696965254592,536870918]],[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____",1696965254592,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u6525a286-b909-409d-87b9-9b0d987dc061logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Klogseq____",1696965254590,536870918]],[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____",1696965254590,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u6525a286-b7da-4f23-addc-d15caaa86b6clogseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^Klogseq____",1696965254591,536870918]],[logseq____"^15logseq____",[36,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ylogseq____",logseq____"fixmelogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^11logseq____",logseq____"FIXMElogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Blogseq____",1696965254591,536870918]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u6525a286-a215-4cb1-980f-e5433b94ccdclogseq____",536870921]],[logseq____"^15logseq____",[37,logseq____"^Klogseq____",1696965254594,536870918]],[logseq____"^15logseq____",[37,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[37,logseq____"^Ylogseq____",logseq____"pq-formellogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^11logseq____",logseq____"pq-Formellogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Blogseq____",1696965254594,536870918]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u6525a286-d731-4650-95ee-aa9ba324a363logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Klogseq____",1696965254592,536870918]],[logseq____"^15logseq____",[38,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ylogseq____",logseq____"nennerlogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^11logseq____",logseq____"Nennerlogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Blogseq____",1696965254592,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u6525a286-9182-40c2-80ca-fc766341d661logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Flogseq____",75,536870918]],[logseq____"^15logseq____",[39,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",1],536870918]],[logseq____"^15logseq____",[39,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[39,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[39,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u6525a286-11c2-41c7-81cb-6ece1b201983logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Flogseq____",49,536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",74,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[40,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[40,logseq____"^Hlogseq____",28,536870918]],[logseq____"^15logseq____",[40,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u6525a286-c15d-4bdc-a9f4-7fa262ef9b49logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Flogseq____",55,536870918]],[logseq____"^15logseq____",[41,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[41,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[41,logseq____"^Hlogseq____",30,536870918]],[logseq____"^15logseq____",[41,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u6525a286-a20b-4fc6-bb6a-4d359a586c18logseq____",536870918]],[logseq____"^15logseq____",[42,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____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[42,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^Vlogseq____",40,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u6525a286-dc62-448d-aca6-0ce8b9d9a5f8logseq____",536870918]],[logseq____"^15logseq____",[43,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____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Flogseq____",68,536870918]],[logseq____"^15logseq____",[43,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^Vlogseq____",68,536870918]],[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____"~u6525a286-1a1d-4d2b-b5ca-49b7e7094752logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",46,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[44,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[44,logseq____"^Hlogseq____",26,536870918]],[logseq____"^15logseq____",[44,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u6525a286-7026-406b-b1b2-ff5ef4319c4flogseq____",536870918]],[logseq____"^15logseq____",[45,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____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",74,536870918]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",74,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u6525a286-8366-42cb-91a4-e04c650f008alogseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[46,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[46,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[46,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[46,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u6525a286-5c76-4b2a-8f12-6dc90e595b46logseq____",536870918]],[logseq____"^15logseq____",[47,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____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",72,536870918]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",75,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u6525a286-1087-48b7-b66d-8e7fd5b585fdlogseq____",536870918]],[logseq____"^15logseq____",[48,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____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",67,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[48,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u6525a286-46cf-4722-a377-014b365bbc44logseq____",536870918]],[logseq____"^15logseq____",[49,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____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",45,536870918]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",74,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u6525a286-d3f5-47e3-9ca1-061b6748af3clogseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",39,536870918]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[50,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u6525a286-6bbd-4459-9cd4-363ba360733clogseq____",536870918]],[logseq____"^15logseq____",[51,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____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",65,536870918]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",41,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u6525a286-206d-4f93-8c6b-049f1a955a86logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",40,536870918]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",40,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",33,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^Hlogseq____",33,536870918]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u6525a286-ccf6-488a-9404-646dd2079af6logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",76,536870918]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",76,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[53,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u6525a286-b1c1-4633-b3f5-c8a610730c0alogseq____",536870918]],[logseq____"^15logseq____",[54,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____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",56,536870918]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",56,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u6525a286-85e2-4c1c-b97a-fb2c368ed5bflogseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",50,536870918]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[55,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[55,logseq____"^Hlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u6525a286-ec1c-4fe6-89ef-663c01082152logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[56,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6525a286-1a15-49cd-b256-86bfa7a7e993logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",77,536870918]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",67,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",34,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[57,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[57,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",34,536870918]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",38,536870918]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u6525a286-7d03-4e7d-89fa-ce8cbc2a1e75logseq____",536870918]],[logseq____"^15logseq____",[58,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____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",48,536870918]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",67,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u6525a286-60f4-4ade-9fe4-2851645ddf78logseq____",536870918]],[logseq____"^15logseq____",[59,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____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",43,536870918]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",68,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",24,536870918]],[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____"~u6525a286-250a-400b-9c2e-4776054f942flogseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",39,536870918]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",39,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6525a286-2f28-4a75-8ce6-bba2d61530bblogseq____",536870918]],[logseq____"^15logseq____",[61,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____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",54,536870918]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",56,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u6525a286-2850-43c5-a918-f74dd5314bd2logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",78,536870918]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",78,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",24,536870918]],[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____"~u6525a286-c89b-4b46-976a-fc8ce3ee6fc2logseq____",536870918]],[logseq____"^15logseq____",[63,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____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",55,536870918]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",55,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6525a286-ad93-4f84-a18b-d3816f53a9b9logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",70,536870918]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",70,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u6525a286-9ae4-4191-b343-6f2e135f35dflogseq____",536870918]],[logseq____"^15logseq____",[65,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____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",41,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6525a286-c84e-4b4b-9a87-5a72785f2759logseq____",536870918]],[logseq____"^15logseq____",[66,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____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",60,536870918]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",39,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u6525a286-7bd7-4eec-be4b-1460d09043e5logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",68,536870918]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",46,536870918]],[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____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[67,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u6525a286-cc42-494b-badf-16a24a456b8clogseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",46,536870918]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",46,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[68,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[68,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u6525a286-7391-4b11-a541-d3e0b76cfaeflogseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",49,536870918]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",49,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[69,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u6525a286-509d-4712-9d82-15c2db63671alogseq____",536870918]],[logseq____"^15logseq____",[70,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____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",58,536870918]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",67,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u6525a286-aefb-4f38-bcd6-67c0a0a001f1logseq____",536870918]],[logseq____"^15logseq____",[71,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____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",50,536870918]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",50,536870918]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u6525a286-a87c-42f8-961a-6a8a94b429b0logseq____",536870918]],[logseq____"^15logseq____",[72,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____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",75,536870918]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",75,536870918]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u6525a286-d2e0-4457-9c17-735891d3ab35logseq____",536870918]],[logseq____"^15logseq____",[73,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____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",81,536870918]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",57,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",34,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u6525a286-9be8-42f7-a9a8-2f6c0fc905c1logseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",51,536870918]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",41,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[74,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",25,536870918]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u6525a286-3aff-4f8c-9fac-b84c3e7173d9logseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",56,536870918]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[75,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",27,536870918]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u6525a286-e3c6-479a-899c-ed860b007076logseq____",536870918]],[logseq____"^15logseq____",[76,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____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",63,536870918]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",55,536870918]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u6525a286-9cb2-45cd-ad81-afd70503525clogseq____",536870918]],[logseq____"^15logseq____",[77,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____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",70,536870918]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",67,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u6525a286-3748-4377-833c-cecd3f974de2logseq____",536870918]],[logseq____"^15logseq____",[78,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____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",59,536870918]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",68,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u6525a286-d1b1-4d18-b8f9-8519c2b40b28logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",80,536870918]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",80,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",37,536870918]],[logseq____"^15logseq____",[79,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u6525a286-b9b6-42e0-95e1-497e5a7a7910logseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"## 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istlogseq____",536870921]],[logseq____"^15logseq____",[125,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[125,logseq____"^Flogseq____",132,536870921]],[logseq____"^15logseq____",[125,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[125,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",105,536870921]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[125,logseq____"^Hlogseq____",105,536870921]],[logseq____"^15logseq____",[125,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[125,logseq____"^;logseq____",logseq____"~u6525a286-86f1-4945-8184-08ea633346a5logseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Flogseq____",125,536870921]],[logseq____"^15logseq____",[126,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[126,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",98,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",115,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",98,536870921]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",107,536870921]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",115,536870921]],[logseq____"^15logseq____",[126,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[126,logseq____"^;logseq____",logseq____"~u6525a286-b0cb-4ad0-b41a-585143f3e884logseq____",536870921]],[logseq____"^15logseq____",[127,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____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Flogseq____",135,536870921]],[logseq____"^15logseq____",[127,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[127,logseq____"^Vlogseq____",135,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",102,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[127,logseq____"^Hlogseq____",102,536870921]],[logseq____"^15logseq____",[127,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[127,logseq____"^;logseq____",logseq____"~u6525a286-a734-4f6e-98b2-5d5e73ae9fcalogseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", jetzt die [[Semantik]]. Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Flogseq____",124,536870921]],[logseq____"^15logseq____",[128,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[128,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",102,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",106,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",109,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",113,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[128,logseq____"^Hlogseq____",102,536870921]],[logseq____"^15logseq____",[128,logseq____"^Hlogseq____",106,536870921]],[logseq____"^15logseq____",[128,logseq____"^Hlogseq____",109,536870921]],[logseq____"^15logseq____",[128,logseq____"^Hlogseq____",113,536870921]],[logseq____"^15logseq____",[128,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[128,logseq____"^;logseq____",logseq____"~u6525a286-0143-4a11-bffa-175764c35426logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Flogseq____",126,536870921]],[logseq____"^15logseq____",[129,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[129,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",104,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[129,logseq____"^Hlogseq____",104,536870921]],[logseq____"^15logseq____",[129,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[129,logseq____"^;logseq____",logseq____"~u6525a286-5299-46b0-823e-fc3000a5fd85logseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Qlogseq____",logseq____"[[Aussagenlogische variable]]: [[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Flogseq____",128,536870921]],[logseq____"^15logseq____",[130,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[130,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",99,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",108,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[130,logseq____"^Hlogseq____",99,536870921]],[logseq____"^15logseq____",[130,logseq____"^Hlogseq____",108,536870921]],[logseq____"^15logseq____",[130,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[130,logseq____"^;logseq____",logseq____"~u6525a286-855c-4c82-96d7-1f36b2828c2alogseq____",536870921]],[logseq____"^15logseq____",[131,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____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Flogseq____",136,536870921]],[logseq____"^15logseq____",[131,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[131,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",98,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",101,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",102,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",109,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[131,logseq____"^Hlogseq____",98,536870921]],[logseq____"^15logseq____",[131,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[131,logseq____"^;logseq____",logseq____"~u6525a286-688e-46da-b919-ac4b0a049f6alogseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Qlogseq____",logseq____"[[Tantologie]]: Formel, die konstant $w$ istlogseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Flogseq____",136,536870921]],[logseq____"^15logseq____",[132,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[132,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",104,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[132,logseq____"^Hlogseq____",104,536870921]],[logseq____"^15logseq____",[132,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[132,logseq____"^;logseq____",logseq____"~u6525a286-fe57-43f5-b36e-ef3b02fdd03blogseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Flogseq____",119,536870921]],[logseq____"^15logseq____",[133,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[133,logseq____"^Vlogseq____",118,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",100,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[133,logseq____"^Hlogseq____",100,536870921]],[logseq____"^15logseq____",[133,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[133,logseq____"^;logseq____",logseq____"~u6525a286-d6eb-42a6-8f17-22b028af6a24logseq____",536870921]],[logseq____"^15logseq____",[134,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____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Flogseq____",120,536870921]],[logseq____"^15logseq____",[134,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[134,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[134,logseq____"^Hlogseq____",110,536870921]],[logseq____"^15logseq____",[134,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[134,logseq____"^;logseq____",logseq____"~u6525a286-ca3c-4031-a906-a67d47a83a28logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Flogseq____",118,536870921]],[logseq____"^15logseq____",[135,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[135,logseq____"^Vlogseq____",117,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[135,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870921]],[logseq____"^15logseq____",[135,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[135,logseq____"^Hlogseq____",110,536870921]],[logseq____"^15logseq____",[135,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[135,logseq____"^;logseq____",logseq____"~u6525a286-abe9-4509-951d-44207f1e8f2blogseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Qlogseq____",logseq____"[[Wahrheitswerteverlauf]] einer [[Aussageformel]]: Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Flogseq____",123,536870921]],[logseq____"^15logseq____",[136,logseq____"^Xlogseq____",117,536870921]],[logseq____"^15logseq____",[136,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",98,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",101,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",102,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",109,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[136,logseq____"^Hlogseq____",98,536870921]],[logseq____"^15logseq____",[136,logseq____"^Hlogseq____",101,536870921]],[logseq____"^15logseq____",[136,logseq____"^Hlogseq____",102,536870921]],[logseq____"^15logseq____",[136,logseq____"^Hlogseq____",109,536870921]],[logseq____"^15logseq____",[136,logseq____"^Hlogseq____",112,536870921]],[logseq____"^15logseq____",[136,logseq____"^Hlogseq____",116,536870921]],[logseq____"^15logseq____",[136,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[136,logseq____"^;logseq____",logseq____"~u6525a286-0f12-4190-9bff-900eb5b69184logseq____",536870921]],[logseq____"^15logseq____",[137,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 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