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themelogseq____",536870918]],[logseq____"^15logseq____",[29,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[29,logseq____"^Flogseq____",28,536870918]],[logseq____"^15logseq____",[29,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[29,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[29,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[29,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[29,logseq____"^;logseq____",logseq____"~u6525668b-2579-46ff-93d1-eca8fdce92a0logseq____",536870918]],[logseq____"^15logseq____",[30,logseq____"^Qlogseq____",logseq____"### Manual\\n\\n1. Enable Logseq developer mode (Settings → Advanced → Developer mode)\\n2. Clone this repository\\n3. Logseq plugins → Load unpacked plugin → select the folder with cloned repository\\n4. Logseq → Themes → Tensetlogseq____",536870918]],[logseq____"^15logseq____",[30,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[30,logseq____"^Flogseq____",29,536870918]],[logseq____"^15logseq____",[30,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[30,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[30,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[30,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870918]],[logseq____"^15logseq____",[30,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[30,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[30,logseq____"^;logseq____",logseq____"~u6525668b-54a5-4b84-857c-fa3571967bcflogseq____",536870918]],[logseq____"^15logseq____",[31,logseq____"^Qlogseq____",logseq____"## How to build\\n\\n1. Install node v18.15.0. If you use `nvm`, you can also run `nvm use` inside the project directory.\\n\\n2. Install dependencies with `npm i`\\n\\n3. Build with `npm run build`logseq____",536870918]],[logseq____"^15logseq____",[31,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[31,logseq____"^Flogseq____",30,536870918]],[logseq____"^15logseq____",[31,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[31,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[31,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[31,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[31,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[31,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[31,logseq____"^;logseq____",logseq____"~u6525668b-f9b9-45f1-ac23-f38098028e9dlogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Klogseq____",1696949899738,536870920]],[logseq____"^15logseq____",[34,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[34,logseq____"^Ylogseq____",logseq____"potenzenlogseq____",536870920]],[logseq____"^15logseq____",[34,logseq____"^11logseq____",logseq____"Potenzenlogseq____",536870920]],[logseq____"^15logseq____",[34,logseq____"^Blogseq____",1696949899738,536870920]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u6525668b-88f8-4d12-86ef-9d38d746475blogseq____",536870920]],[logseq____"^15logseq____",[35,logseq____"^Klogseq____",1696949899729,536870920]],[logseq____"^15logseq____",[35,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[35,logseq____"^Ylogseq____",logseq____"pascalsches dreiecklogseq____",536870920]],[logseq____"^15logseq____",[35,logseq____"^11logseq____",logseq____"Pascalsches Dreiecklogseq____",536870920]],[logseq____"^15logseq____",[35,logseq____"^Blogseq____",1696949899729,536870920]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u6525668b-83af-4df1-983f-f5b6b32547a7logseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^Klogseq____",1696949899723,536870920]],[logseq____"^15logseq____",[36,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[36,logseq____"^Ylogseq____",logseq____"logarithmenlogseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^11logseq____",logseq____"Logarithmenlogseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^Blogseq____",1696949899723,536870920]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u6525668c-f9cd-4f86-972d-76617da8af6elogseq____",536870924]],[logseq____"^15logseq____",[37,logseq____"^Klogseq____",1696949899736,536870920]],[logseq____"^15logseq____",[37,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[37,logseq____"^Ylogseq____",logseq____"binomialkoeffizientlogseq____",536870920]],[logseq____"^15logseq____",[37,logseq____"^11logseq____",logseq____"Binomialkoeffizientlogseq____",536870920]],[logseq____"^15logseq____",[37,logseq____"^Blogseq____",1696949899736,536870920]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u6525668b-a37e-4f2c-91db-24a8ba675abblogseq____",536870920]],[logseq____"^15logseq____",[38,logseq____"^Klogseq____",1696949899728,536870920]],[logseq____"^15logseq____",[38,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[38,logseq____"^Ylogseq____",logseq____"binomische formelnlogseq____",536870920]],[logseq____"^15logseq____",[38,logseq____"^11logseq____",logseq____"Binomische Formelnlogseq____",536870920]],[logseq____"^15logseq____",[38,logseq____"^Blogseq____",1696949899728,536870920]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u6525668b-a3ac-4c1a-b0e4-782750dc5061logseq____",536870920]],[logseq____"^15logseq____",[39,logseq____"^Klogseq____",1696949899726,536870920]],[logseq____"^15logseq____",[39,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[39,logseq____"^Ylogseq____",logseq____"trigonometrielogseq____",536870920]],[logseq____"^15logseq____",[39,logseq____"^11logseq____",logseq____"Trigonometrielogseq____",536870920]],[logseq____"^15logseq____",[39,logseq____"^Blogseq____",1696949899726,536870920]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u6525668b-350a-4aec-9485-1bcd2682e625logseq____",536870920]],[logseq____"^15logseq____",[40,logseq____"^Klogseq____",1696949899738,536870920]],[logseq____"^15logseq____",[40,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[40,logseq____"^Ylogseq____",logseq____"wurzelnlogseq____",536870920]],[logseq____"^15logseq____",[40,logseq____"^11logseq____",logseq____"Wurzelnlogseq____",536870920]],[logseq____"^15logseq____",[40,logseq____"^Blogseq____",1696949899738,536870920]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u6525668b-cd07-479f-af67-ace586312053logseq____",536870920]],[logseq____"^15logseq____",[41,logseq____"^Klogseq____",1696949899738,536870920]],[logseq____"^15logseq____",[41,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[41,logseq____"^Ylogseq____",logseq____"pascalsche dreiecklogseq____",536870920]],[logseq____"^15logseq____",[41,logseq____"^11logseq____",logseq____"Pascalsche Dreiecklogseq____",536870920]],[logseq____"^15logseq____",[41,logseq____"^Blogseq____",1696949899738,536870920]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u6525668b-8c97-4002-b3fd-2f7c681228aclogseq____",536870920]],[logseq____"^15logseq____",[42,logseq____"^Klogseq____",1696949899739,536870920]],[logseq____"^15logseq____",[42,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[42,logseq____"^Ylogseq____",logseq____"auffrischung mathe 1logseq____",536870920]],[logseq____"^15logseq____",[42,logseq____"^11logseq____",logseq____"Auffrischung Mathe 1logseq____",536870920]],[logseq____"^15logseq____",[42,logseq____"^Blogseq____",1696949899739,536870920]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u6525668b-d6f7-4942-b461-37a2e48429d6logseq____",536870921]],[logseq____"^15logseq____",[43,logseq____"^Klogseq____",1696949899740,536870920]],[logseq____"^15logseq____",[43,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[43,logseq____"^Ylogseq____",logseq____"fixmelogseq____",536870920]],[logseq____"^15logseq____",[43,logseq____"^11logseq____",logseq____"FIXMElogseq____",536870920]],[logseq____"^15logseq____",[43,logseq____"^Blogseq____",1696949899740,536870920]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u6525668c-80a9-4a99-b017-eb13842505eblogseq____",536870922]],[logseq____"^15logseq____",[44,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870920]],[logseq____"^15logseq____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",51,536870920]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",34,536870920]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[44,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[44,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[44,logseq____"^Hlogseq____",34,536870920]],[logseq____"^15logseq____",[44,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u6525668b-37bd-411d-b8ea-72b7ce236c91logseq____",536870920]],[logseq____"^15logseq____",[45,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____",536870920]],[logseq____"^15logseq____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",50,536870920]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[45,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[45,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u6525668b-7509-4b2e-8ea3-0bf2a149e76clogseq____",536870920]],[logseq____"^15logseq____",[46,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870920]],[logseq____"^15logseq____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",66,536870920]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[46,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[46,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[46,logseq____"^Hlogseq____",37,536870920]],[logseq____"^15logseq____",[46,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u6525668b-e71b-4118-ba36-a1bc0a1a7195logseq____",536870920]],[logseq____"^15logseq____",[47,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____",536870920]],[logseq____"^15logseq____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",44,536870920]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[47,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u6525668b-e813-4af1-860f-c9ae0ea65beelogseq____",536870920]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",70,536870920]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u6525668b-bcf1-4dcd-ade2-a1f29ce99339logseq____",536870920]],[logseq____"^15logseq____",[49,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____",536870920]],[logseq____"^15logseq____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",52,536870920]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u6525668b-f786-4500-b588-16d597841818logseq____",536870920]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870920]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",55,536870920]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[50,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[50,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[50,logseq____"^Hlogseq____",40,536870920]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u6525668b-453e-4966-b892-bad078a8c20flogseq____",536870920]],[logseq____"^15logseq____",[51,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____",536870920]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",61,536870920]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u6525668b-83ab-457d-af65-48c54e433e71logseq____",536870920]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870920]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",53,536870920]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[52,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[52,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[52,logseq____"^Hlogseq____",35,536870920]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u6525668b-7c47-4bd5-837a-d7a138284ad1logseq____",536870920]],[logseq____"^15logseq____",[53,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____",536870920]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",58,536870920]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u6525668b-035e-41d6-8ef8-d5c06c2b670flogseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"![draws/2023-10-08-21-23-31.excalidraw](../assets/excalidraw_svg/2023-10-08-21-23-31.svg)logseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",48,536870920]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u6525668b-d6c6-464a-b28d-8a6923f96259logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",77,536870920]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u6525668b-6d42-439d-adeb-e44952cbe7d0logseq____",536870920]],[logseq____"^15logseq____",[56,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____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",60,536870920]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6525668b-9c99-4ad7-9462-0f2ef37cfc30logseq____",536870920]],[logseq____"^15logseq____",[57,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____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",65,536870920]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u6525668b-5c09-4f6e-9279-6d10f937e887logseq____",536870920]],[logseq____"^15logseq____",[58,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____",536870920]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",72,536870920]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u6525668b-e733-446a-8782-eb925704c38alogseq____",536870920]],[logseq____"^15logseq____",[59,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____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",49,536870920]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u6525668b-154a-4881-adc9-59cd8c28aa52logseq____",536870920]],[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____",536870920]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",71,536870920]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6525668b-ff9f-4c0d-ac07-a5221ce74ee6logseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",46,536870920]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",41,536870920]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u6525668b-c52c-42c5-8e15-10a9bde6362clogseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",69,536870920]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",39,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[62,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[62,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",39,536870920]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u6525668b-f007-4055-9eaa-5edaf01a5236logseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{y^2}\\\\notag\\\\\\\\\\nlogseq____&=\\\\left|y\\\\right|\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",76,536870920]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6525668b-1a14-4061-964a-1e09dfbd6a79logseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",75,536870920]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u6525668b-999b-4f7e-ab46-eb381ffe78bblogseq____",536870920]],[logseq____"^15logseq____",[65,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____",536870920]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",68,536870920]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6525668b-fd56-4a3a-8c3d-361b728acd60logseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",59,536870920]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[66,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u6525668b-8c08-41ac-ab0e-f961929eedb4logseq____",536870920]],[logseq____"^15logseq____",[67,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____",536870920]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",47,536870920]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u6525668b-6f00-400c-9e2a-de4320db2f12logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",54,536870920]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[68,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[68,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[68,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u6525668b-864a-40f4-9b19-ddc210519b51logseq____",536870920]],[logseq____"^15logseq____",[69,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____",536870920]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",78,536870920]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u6525668b-c508-43f7-b03d-f4af1f8bac12logseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",42,536870920]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",34,536870920]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[70,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[70,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[70,logseq____"^Hlogseq____",34,536870920]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",false,536870920]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u6525668b-4740-41c4-bb20-16f734ea025alogseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",57,536870920]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[71,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[71,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[71,logseq____"^Hlogseq____",40,536870920]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u6525668b-7e50-49bb-b5b0-4b584f24ea70logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",64,536870920]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[72,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[72,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[72,logseq____"^Hlogseq____",38,536870920]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u6525668b-f26c-4ace-8fb7-0a10ce8629d7logseq____",536870920]],[logseq____"^15logseq____",[73,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____",536870920]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",62,536870920]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u6525668b-896d-4d6c-b520-63acb3c501b6logseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",63,536870920]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u6525668b-b7b1-4824-b1f2-98922b606972logseq____",536870920]],[logseq____"^15logseq____",[75,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____",536870920]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",73,536870920]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u6525668b-10bf-48b5-bf5a-947b091668felogseq____",536870920]],[logseq____"^15logseq____",[76,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____",536870920]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",45,536870920]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u6525668b-5514-4571-9493-c98935988eb9logseq____",536870920]],[logseq____"^15logseq____",[77,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____",536870920]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",67,536870920]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u6525668b-c811-4fff-905b-088c3636da96logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",56,536870920]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",42,536870920]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",42,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[78,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[78,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u6525668b-eb90-4904-b52a-b3eacb47f053logseq____",536870920]],[logseq____"^15logseq____",[80,logseq____"^Klogseq____",1696949899857,536870921]],[logseq____"^15logseq____",[80,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[80,logseq____"^Ylogseq____",logseq____"auffrischung mathelogseq____",536870921]],[logseq____"^15logseq____",[80,logseq____"^11logseq____",logseq____"Auffrischung Mathelogseq____",536870921]],[logseq____"^15logseq____",[80,logseq____"^Blogseq____",1696949899857,536870921]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u6525668c-bcc1-4112-9750-7293057ea32elogseq____",536870928]],[logseq____"^15logseq____",[81,logseq____"^Klogseq____",1696949899858,536870921]],[logseq____"^15logseq____",[81,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[81,logseq____"^Ylogseq____",logseq____"auffrischung mathe 2logseq____",536870921]],[logseq____"^15logseq____",[81,logseq____"^11logseq____",logseq____"Auffrischung Mathe 2logseq____",536870921]],[logseq____"^15logseq____",[81,logseq____"^Blogseq____",1696949899858,536870921]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u6525668b-24ce-47b4-ada7-807e060699b6logseq____",536870921]],[logseq____"^15logseq____",[82,logseq____"^Klogseq____",1696949899859,536870921]],[logseq____"^15logseq____",[82,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[82,logseq____"^Ylogseq____",logseq____"auffrischung mathe 3logseq____",536870921]],[logseq____"^15logseq____",[82,logseq____"^11logseq____",logseq____"Auffrischung Mathe 3logseq____",536870921]],[logseq____"^15logseq____",[82,logseq____"^Blogseq____",1696949899859,536870921]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u6525668b-a57d-4f64-9aab-75a2f2d4a908logseq____",536870921]],[logseq____"^15logseq____",[83,logseq____"^Qlogseq____",logseq____"[[Auffrischung Mathe 1]]logseq____",536870921]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",80,536870921]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",80,536870921]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",80,536870921]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",42,536870921]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",80,536870921]],[logseq____"^15logseq____",[83,logseq____"^Hlogseq____",42,536870921]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u6525668b-6d51-428b-a9ac-4889160d46f8logseq____",536870921]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"[[Auffrischung Mathe 2]]logseq____",536870921]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",83,536870921]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",80,536870921]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",80,536870921]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",80,536870921]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",81,536870921]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",81,536870921]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u6525668b-ab9c-4901-ae6b-ccf33e44a7f2logseq____",536870921]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"[[Auffrischung Mathe 3]]logseq____",536870921]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",84,536870921]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",80,536870921]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",80,536870921]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",80,536870921]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",82,536870921]],[logseq____"^15logseq____",[85,logseq____"^Hlogseq____",82,536870921]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u6525668b-cb9a-42a9-97af-acbef2f37109logseq____",536870921]],[logseq____"^15logseq____",[87,logseq____"^Klogseq____",1696949900047,536870922]],[logseq____"^15logseq____",[87,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[87,logseq____"^Ylogseq____",logseq____"wahrheitswerteverlauflogseq____",536870922]],[logseq____"^15logseq____",[87,logseq____"^11logseq____",logseq____"Wahrheitswerteverlauflogseq____",536870922]],[logseq____"^15logseq____",[87,logseq____"^Blogseq____",1696949900047,536870922]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u6525668c-06cf-48c8-b523-b5d2ddc0aa9alogseq____",536870922]],[logseq____"^15logseq____",[88,logseq____"^Klogseq____",1696949900039,536870922]],[logseq____"^15logseq____",[88,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[88,logseq____"^Ylogseq____",logseq____"aussagenlogische variablelogseq____",536870922]],[logseq____"^15logseq____",[88,logseq____"^11logseq____",logseq____"Aussagenlogische variablelogseq____",536870922]],[logseq____"^15logseq____",[88,logseq____"^Blogseq____",1696949900039,536870922]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u6525668c-e29f-484f-aa08-282211bda214logseq____",536870922]],[logseq____"^15logseq____",[89,logseq____"^Klogseq____",1696949900033,536870922]],[logseq____"^15logseq____",[89,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[89,logseq____"^Ylogseq____",logseq____"wikipedialogseq____",536870922]],[logseq____"^15logseq____",[89,logseq____"^11logseq____",logseq____"Wikipedialogseq____",536870922]],[logseq____"^15logseq____",[89,logseq____"^Blogseq____",1696949900033,536870922]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u6525668c-a3a9-4b61-a181-3c40ce214e99logseq____",536870922]],[logseq____"^15logseq____",[90,logseq____"^Klogseq____",1696949900044,536870922]],[logseq____"^15logseq____",[90,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[90,logseq____"^Ylogseq____",logseq____"formellogseq____",536870922]],[logseq____"^15logseq____",[90,logseq____"^11logseq____",logseq____"Formellogseq____",536870922]],[logseq____"^15logseq____",[90,logseq____"^Blogseq____",1696949900044,536870922]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u6525668c-b4f3-4fb1-a273-97e8f5f1fbb1logseq____",536870922]],[logseq____"^15logseq____",[91,logseq____"^Klogseq____",1696949900044,536870922]],[logseq____"^15logseq____",[91,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[91,logseq____"^Ylogseq____",logseq____"wahrheitswertlogseq____",536870922]],[logseq____"^15logseq____",[91,logseq____"^11logseq____",logseq____"Wahrheitswertlogseq____",536870922]],[logseq____"^15logseq____",[91,logseq____"^Blogseq____",1696949900044,536870922]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u6525668c-25f6-4ce8-80f0-4354bf1ed583logseq____",536870922]],[logseq____"^15logseq____",[92,logseq____"^Klogseq____",1696949900032,536870922]],[logseq____"^15logseq____",[92,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[92,logseq____"^Ylogseq____",logseq____"\\logseq____"mathematische grundlagen der informatik\\logseq____", 5. auflage 2011logseq____",536870922]],[logseq____"^15logseq____",[92,logseq____"^11logseq____",logseq____"\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011logseq____",536870922]],[logseq____"^15logseq____",[92,logseq____"^Blogseq____",1696949900032,536870922]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u6525668c-6bab-4931-9810-154efe7a07e2logseq____",536870922]],[logseq____"^15logseq____",[93,logseq____"^Klogseq____",1696949900048,536870922]],[logseq____"^15logseq____",[93,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[93,logseq____"^Ylogseq____",logseq____"tantologielogseq____",536870922]],[logseq____"^15logseq____",[93,logseq____"^11logseq____",logseq____"Tantologielogseq____",536870922]],[logseq____"^15logseq____",[93,logseq____"^Blogseq____",1696949900048,536870922]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u6525668c-62ba-4e7e-a342-d2c2a8d95356logseq____",536870922]],[logseq____"^15logseq____",[94,logseq____"^Klogseq____",1696949900046,536870922]],[logseq____"^15logseq____",[94,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[94,logseq____"^Ylogseq____",logseq____"kontradiktionlogseq____",536870922]],[logseq____"^15logseq____",[94,logseq____"^11logseq____",logseq____"Kontradiktionlogseq____",536870922]],[logseq____"^15logseq____",[94,logseq____"^Blogseq____",1696949900046,536870922]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u6525668c-bd84-4225-aa8f-b069dfbaa9f9logseq____",536870922]],[logseq____"^15logseq____",[95,logseq____"^Klogseq____",1696949900037,536870922]],[logseq____"^15logseq____",[95,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[95,logseq____"^Ylogseq____",logseq____"semantiklogseq____",536870922]],[logseq____"^15logseq____",[95,logseq____"^11logseq____",logseq____"Semantiklogseq____",536870922]],[logseq____"^15logseq____",[95,logseq____"^Blogseq____",1696949900037,536870922]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u6525668c-39a6-4436-a9c9-a48ed61b6fb7logseq____",536870922]],[logseq____"^15logseq____",[96,logseq____"^Klogseq____",1696949900048,536870922]],[logseq____"^15logseq____",[96,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[96,logseq____"^Ylogseq____",logseq____"logisch 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und diskrete strukturen 1logseq____",536870922]],[logseq____"^15logseq____",[106,logseq____"^11logseq____",logseq____"Grundlagen und Diskrete Strukturen 1logseq____",536870922]],[logseq____"^15logseq____",[106,logseq____"^Blogseq____",1696949900031,536870922]],[logseq____"^15logseq____",[106,logseq____"^;logseq____",logseq____"~u6525668c-7bc8-4a2b-8680-c605a79fc339logseq____",536870923]],[logseq____"^15logseq____",[107,logseq____"^Qlogseq____",logseq____"[[Belegung]] (der Variablen): Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[107,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[107,logseq____"^Flogseq____",109,536870922]],[logseq____"^15logseq____",[107,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[107,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",97,536870922]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",101,536870922]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",105,536870922]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",97,536870922]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",101,536870922]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",105,536870922]],[logseq____"^15logseq____",[107,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[107,logseq____"^;logseq____",logseq____"~u6525668b-6186-484d-9d1e-ccf8404d8a19logseq____",536870922]],[logseq____"^15logseq____",[108,logseq____"^Qlogseq____",logseq____"[[Wahrheitswerteverlauf]] einer [[Aussageformel]]: Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870922]],[logseq____"^15logseq____",[108,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[108,logseq____"^Flogseq____",107,536870922]],[logseq____"^15logseq____",[108,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[108,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",87,536870922]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",90,536870922]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",91,536870922]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",98,536870922]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",101,536870922]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",105,536870922]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[108,logseq____"^Hlogseq____",87,536870922]],[logseq____"^15logseq____",[108,logseq____"^Hlogseq____",90,536870922]],[logseq____"^15logseq____",[108,logseq____"^Hlogseq____",91,536870922]],[logseq____"^15logseq____",[108,logseq____"^Hlogseq____",98,536870922]],[logseq____"^15logseq____",[108,logseq____"^Hlogseq____",101,536870922]],[logseq____"^15logseq____",[108,logseq____"^Hlogseq____",105,536870922]],[logseq____"^15logseq____",[108,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[108,logseq____"^;logseq____",logseq____"~u6525668b-f74f-4c62-9632-9d658922ece3logseq____",536870922]],[logseq____"^15logseq____",[109,logseq____"^Qlogseq____",logseq____"[[Aussageformel]]: Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt 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ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\n\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\\\\\\\n(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\notag\\\\\\\\\\n\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\n\\\\text{ hat eine Lösung }x,y,z\\\\notag\\n\\\\\\\\\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nx^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nx,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\n\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\n\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\n\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[111,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[111,logseq____"^Flogseq____",127,536870922]],[logseq____"^15logseq____",[111,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[111,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[111,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[111,logseq____"^;logseq____",logseq____"~u6525668c-ea1d-4d11-ad78-ba71c344381alogseq____",536870922]],[logseq____"^15logseq____",[112,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870922]],[logseq____"^15logseq____",[112,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[112,logseq____"^Flogseq____",106,536870922]],[logseq____"^15logseq____",[112,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[112,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[112,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[112,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[112,logseq____"^17logseq____",false,536870922]],[logseq____"^15logseq____",[112,logseq____"^;logseq____",logseq____"~u6525668c-24b1-4153-8bc5-37a13a91b58alogseq____",536870922]],[logseq____"^15logseq____",[113,logseq____"^Qlogseq____",logseq____"[[Tantologie]]: Formel, die konstant $w$ istlogseq____",536870922]],[logseq____"^15logseq____",[113,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[113,logseq____"^Flogseq____",125,536870922]],[logseq____"^15logseq____",[113,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[113,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[113,logseq____"^Ulogseq____",93,536870922]],[logseq____"^15logseq____",[113,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[113,logseq____"^Hlogseq____",93,536870922]],[logseq____"^15logseq____",[113,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[113,logseq____"^;logseq____",logseq____"~u6525668b-b82c-46fc-aac3-a1ec59da4ef2logseq____",536870922]],[logseq____"^15logseq____",[114,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[114,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[114,logseq____"^Flogseq____",126,536870922]],[logseq____"^15logseq____",[114,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[114,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",99,536870922]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[114,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[114,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[114,logseq____"^Hlogseq____",99,536870922]],[logseq____"^15logseq____",[114,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[114,logseq____"^;logseq____",logseq____"~u6525668c-4ccd-416d-b371-72d924c0c101logseq____",536870922]],[logseq____"^15logseq____",[115,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[115,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[115,logseq____"^Flogseq____",111,536870922]],[logseq____"^15logseq____",[115,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[115,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",103,536870922]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[115,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870922]],[logseq____"^15logseq____",[115,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[115,logseq____"^Hlogseq____",103,536870922]],[logseq____"^15logseq____",[115,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[115,logseq____"^;logseq____",logseq____"~u6525668c-d1dc-453c-9bad-4690c8873127logseq____",536870922]],[logseq____"^15logseq____",[116,logseq____"^Qlogseq____",logseq____"[[Aussagenlogische variable]]: [[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____",536870922]],[logseq____"^15logseq____",[116,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[116,logseq____"^Flogseq____",122,536870922]],[logseq____"^15logseq____",[116,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[116,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",88,536870922]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",97,536870922]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[116,logseq____"^Hlogseq____",88,536870922]],[logseq____"^15logseq____",[116,logseq____"^Hlogseq____",97,536870922]],[logseq____"^15logseq____",[116,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[116,logseq____"^;logseq____",logseq____"~u6525668b-5e60-4926-8929-c10c8caf15eflogseq____",536870922]],[logseq____"^15logseq____",[117,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870922]],[logseq____"^15logseq____",[117,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[117,logseq____"^Flogseq____",112,536870922]],[logseq____"^15logseq____",[117,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[117,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",92,536870922]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[117,logseq____"^Hlogseq____",92,536870922]],[logseq____"^15logseq____",[117,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[117,logseq____"^;logseq____",logseq____"~u6525668c-1920-486e-b12b-9b131f805a1clogseq____",536870922]],[logseq____"^15logseq____",[118,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[118,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[118,logseq____"^Flogseq____",121,536870922]],[logseq____"^15logseq____",[118,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[118,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[118,logseq____"^Ulogseq____",93,536870922]],[logseq____"^15logseq____",[118,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[118,logseq____"^Hlogseq____",93,536870922]],[logseq____"^15logseq____",[118,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[118,logseq____"^;logseq____",logseq____"~u6525668b-d1a3-4284-9e6a-2d7e13085d6elogseq____",536870922]],[logseq____"^15logseq____",[119,logseq____"^Qlogseq____",logseq____"Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&\\\\quadlogseq____& (\\logseq____"\\\\text{und}\\logseq____")\\\\\\\\\\n(p\\\\lor q) logseq____&logseq____& (\\logseq____"\\\\text{oder}\\logseq____")\\\\\\\\\\n(\\\\neg p) logseq____&logseq____& (\\logseq____"\\\\text{nicht}\\logseq____")\\\\\\\\\\n(p\\\\rightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{impliziert}\\logseq____")\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{genau dann wenn}\\logseq____")\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[119,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[119,logseq____"^Flogseq____",115,536870922]],[logseq____"^15logseq____",[119,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[119,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",99,536870922]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[119,logseq____"^Hlogseq____",99,536870922]],[logseq____"^15logseq____",[119,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[119,logseq____"^;logseq____",logseq____"~u6525668c-4ef0-4244-9efa-2e88c3b8ca80logseq____",536870922]],[logseq____"^15logseq____",[120,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____",536870922]],[logseq____"^15logseq____",[120,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[120,logseq____"^Flogseq____",118,536870922]],[logseq____"^15logseq____",[120,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[120,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[120,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[120,logseq____"^;logseq____",logseq____"~u6525668b-2079-4b98-95a8-18f764771a7flogseq____",536870922]],[logseq____"^15logseq____",[121,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870922]],[logseq____"^15logseq____",[121,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[121,logseq____"^Flogseq____",123,536870922]],[logseq____"^15logseq____",[121,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[121,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",87,536870922]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",96,536870922]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",104,536870922]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[121,logseq____"^Hlogseq____",87,536870922]],[logseq____"^15logseq____",[121,logseq____"^Hlogseq____",96,536870922]],[logseq____"^15logseq____",[121,logseq____"^Hlogseq____",104,536870922]],[logseq____"^15logseq____",[121,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[121,logseq____"^;logseq____",logseq____"~u6525668b-627a-4a3f-97d5-5506dadaca2alogseq____",536870922]],[logseq____"^15logseq____",[122,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____",536870922]],[logseq____"^15logseq____",[122,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[122,logseq____"^Flogseq____",124,536870922]],[logseq____"^15logseq____",[122,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[122,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",91,536870922]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",95,536870922]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",98,536870922]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",102,536870922]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",91,536870922]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",95,536870922]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",98,536870922]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",102,536870922]],[logseq____"^15logseq____",[122,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[122,logseq____"^;logseq____",logseq____"~u6525668b-fe4d-4884-bf37-af35724792felogseq____",536870922]],[logseq____"^15logseq____",[123,logseq____"^Qlogseq____",logseq____"[[Kontradiktion]]: Formel, die konstant $f$ istlogseq____",536870922]],[logseq____"^15logseq____",[123,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[123,logseq____"^Flogseq____",113,536870922]],[logseq____"^15logseq____",[123,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[123,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",94,536870922]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[123,logseq____"^Hlogseq____",94,536870922]],[logseq____"^15logseq____",[123,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[123,logseq____"^;logseq____",logseq____"~u6525668b-b66d-4604-aed3-72a04cf34a21logseq____",536870922]],[logseq____"^15logseq____",[124,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____",536870922]],[logseq____"^15logseq____",[124,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[124,logseq____"^Flogseq____",119,536870922]],[logseq____"^15logseq____",[124,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[124,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[124,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[124,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[124,logseq____"^;logseq____",logseq____"~u6525668c-fa38-4888-9253-76999407e5celogseq____",536870922]],[logseq____"^15logseq____",[125,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870922]],[logseq____"^15logseq____",[125,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[125,logseq____"^Flogseq____",108,536870922]],[logseq____"^15logseq____",[125,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[125,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",87,536870922]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[125,logseq____"^Hlogseq____",87,536870922]],[logseq____"^15logseq____",[125,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[125,logseq____"^;logseq____",logseq____"~u6525668b-0fbe-467b-a3bc-d5b71cb35528logseq____",536870922]],[logseq____"^15logseq____",[126,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870922]],[logseq____"^15logseq____",[126,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[126,logseq____"^Flogseq____",117,536870922]],[logseq____"^15logseq____",[126,logseq____"^Xlogseq____",106,536870922]],[logseq____"^15logseq____",[126,logseq____"^Vlogseq____",106,536870922]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",89,536870922]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",106,536870922]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",89,536870922]],[logseq____"^15logseq____",[126,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[126,logseq____"^;logseq____",logseq____"~u6525668c-f31b-41d8-b85f-66277cf808d6logseq____",536870922]],[logseq____"^15logseq____",[127,logseq____"^Qlogseq____",logseq____"Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, 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