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[[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",62,536870919]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",96,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[54,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[54,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u65286a89-dff6-4844-b95e-8ac2c89a323clogseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",59,536870919]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[55,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[55,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u65286a89-fa38-405f-ae1e-eaf4d02ea33flogseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel}$\\n$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&= p logseq____&, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&=0\\\\\\\\\\nx^2-7x+12logseq____&=0\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",90,536870919]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",90,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u65286a89-d164-4d26-a127-afa06b3ca2b5logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",61,536870919]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",61,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",33,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",33,536870919]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u65286a89-a48e-4f30-834d-d5a055eadbe6logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel}$\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&=x^2\\\\\\\\\\ny^2-34y+225logseq____&=0\\\\\\\\\\ny_{1,2}logseq____&=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&\\\\rightarrow logseq____&x_1=5;logseq____&x_2=-5\\\\\\\\\\nx^2=9logseq____&\\\\rightarrow logseq____&x_1=3;logseq____&x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",90,536870919]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",64,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u65286a89-8cdd-4ccc-81cb-84b38280a5a4logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",97,536870919]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[59,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[59,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[59,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u65286a89-f800-422c-9ffa-a185c1d488e9logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",48,536870919]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u65286a89-4de6-4f3e-bba1-0e3c1bc7a2a7logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",52,536870919]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[61,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[61,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u65286a89-81fa-402f-b78e-7f08a2e0f710logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",96,536870919]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",96,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[62,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[62,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u65286a89-b08b-4dd9-b0a2-018282438125logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",52,536870919]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",52,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",45,536870919]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u65286a89-fa95-4f4c-a4a4-9abb355bb36flogseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",86,536870919]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",81,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[64,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[64,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u65286a89-88df-4374-8743-68cc6d521108logseq____",536870919]],[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____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",97,536870919]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u65286a89-a64b-4f81-9f37-e63007cb3308logseq____",536870919]],[logseq____"^15logseq____",[66,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____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",70,536870919]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",54,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u65286a89-cd98-4c08-99be-33b4c1ee69b1logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",92,536870919]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",92,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u65286a89-c611-4ada-9807-4fb9edc64c81logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",95,536870919]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",94,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u65286a89-8aca-42a7-8d66-adec3ca776d3logseq____",536870919]],[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____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",55,536870919]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",55,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u65286a89-15c3-444d-a4db-d0752a25857clogseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",72,536870919]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",54,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u65286a89-f594-4a85-8c2b-8c949d57b8ablogseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",85,536870919]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",59,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u65286a89-d337-402f-9c99-dd0a2a4ad368logseq____",536870919]],[logseq____"^15logseq____",[72,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____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",54,536870919]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",54,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[72,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u65286a89-4f2f-4795-a414-e088ebb93b7elogseq____",536870919]],[logseq____"^15logseq____",[73,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____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",76,536870919]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",53,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u65286a89-b54a-4059-8ce2-a373f095e86blogseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",57,536870919]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",61,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u65286a89-d745-458a-b0bb-5457a75864cdlogseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",66,536870919]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",66,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u65286a89-21c6-47f5-9890-4f17c57359dflogseq____",536870919]],[logseq____"^15logseq____",[76,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____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",53,536870919]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",53,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u65286a89-0c4f-4034-9ff3-6ff090651c3clogseq____",536870919]],[logseq____"^15logseq____",[77,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____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",89,536870919]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",89,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u65286a89-0ff4-417b-a7b0-ab6183c66989logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",77,536870919]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",89,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u65286a89-5d0b-48f8-93a8-5ae815c9e320logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",50,536870919]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",62,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u65286a89-f07b-45c0-b75b-c444b2058466logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"https://www.wolframalpha.comlogseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",63,536870919]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",63,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u65286a89-d9ca-40ff-83b1-7e631e2679aalogseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",54,536870919]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",96,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[81,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[81,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[81,logseq____"^Hlogseq____",29,536870919]],[logseq____"^15logseq____",[81,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u65286a89-18bb-42fb-ac55-c981a43057celogseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Qlogseq____",logseq____"$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Flogseq____",47,536870919]],[logseq____"^15logseq____",[82,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[82,logseq____"^Vlogseq____",47,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",38,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[82,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u65286a89-5725-43c8-9a6f-329a7aa84b2clogseq____",536870919]],[logseq____"^15logseq____",[83,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____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",62,536870919]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",62,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u65286a89-50b6-4777-866c-d52a843980d9logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",73,536870919]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",73,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u65286a89-6f68-409b-ad9f-85cf43b8c333logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",59,536870919]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",59,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u65286a89-108e-429f-834b-d291ac9e5254logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nax^2+bx+clogseq____&=0logseq____&|:a\\\\quadlogseq____&a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&= 0\\\\\\\\\\nplogseq____&=\\\\frac ba,logseq____&q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&=0\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",81,536870919]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",81,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u65286a89-0e7f-4bf6-8084-02cc5e165ec2logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"# [[Wurzelgleichung]]logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",81,536870919]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",96,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[87,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[87,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[87,logseq____"^Hlogseq____",30,536870919]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u65286a89-48ee-43f4-acc2-89781c79ccc2logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",55,536870919]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[88,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[88,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[88,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u65286a89-86ea-4dd0-9a7b-53c2be2f06bblogseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",88,536870919]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[89,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[89,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[89,logseq____"^Hlogseq____",34,536870919]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u65286a89-6bb5-47df-97e2-9a27365d5271logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0 logseq____&logseq____& \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&=-p logseq____&logseq____& x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",93,536870919]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",64,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[90,logseq____"^Hlogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u65286a89-74cc-4326-b03e-4b45a46d2946logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",66,536870919]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",54,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u65286a89-279c-4775-af24-d13e1dc60336logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",49,536870919]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",88,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u65286a89-957c-4c2d-9a9c-2957a6e5d344logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",64,536870919]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",64,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",26,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[93,logseq____"^Hlogseq____",26,536870919]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u65286a89-2cdb-4413-96a4-fe6db07c7d64logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",73,536870919]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",53,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[94,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[94,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[94,logseq____"^Hlogseq____",32,536870919]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u65286a89-93e6-43ef-bf41-7540b316c4fblogseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",94,536870919]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",94,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[95,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u65286a89-5784-4c72-a0ec-6a4ee3cd81d8logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Flogseq____",89,536870919]],[logseq____"^15logseq____",[96,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[96,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[96,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[96,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[96,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[96,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[96,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[96,logseq____"^;logseq____",logseq____"~u65286a89-1987-4b75-a485-ad30b90f3c4flogseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Qlogseq____",logseq____"# Wissensabgleich 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äquivalentlogseq____",536870922]],[logseq____"^15logseq____",[153,logseq____"^Blogseq____",1697147530477,536870922]],[logseq____"^15logseq____",[153,logseq____"^;logseq____",logseq____"~u65286a8a-0349-4c33-bea5-6b8433ac9277logseq____",536870922]],[logseq____"^15logseq____",[154,logseq____"^Klogseq____",1697147530473,536870922]],[logseq____"^15logseq____",[154,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[154,logseq____"^Ylogseq____",logseq____"variablelogseq____",536870922]],[logseq____"^15logseq____",[154,logseq____"^11logseq____",logseq____"Variablelogseq____",536870922]],[logseq____"^15logseq____",[154,logseq____"^Blogseq____",1697147530473,536870922]],[logseq____"^15logseq____",[154,logseq____"^;logseq____",logseq____"~u65286a8a-82f8-4e7a-ac0e-1d113ffa6507logseq____",536870922]],[logseq____"^15logseq____",[155,logseq____"^Klogseq____",1697147530474,536870922]],[logseq____"^15logseq____",[155,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[155,logseq____"^Ylogseq____",logseq____"tabellenregelnlogseq____",536870922]],[logseq____"^15logseq____",[155,logseq____"^11logseq____",logseq____"Tabellenregelnlogseq____",536870922]],[logseq____"^15logseq____",[155,logseq____"^Blogseq____",1697147530474,536870922]],[logseq____"^15logseq____",[155,logseq____"^;logseq____",logseq____"~u65286a8a-b8e0-40ae-9ab1-2742b427e1falogseq____",536870922]],[logseq____"^15logseq____",[156,logseq____"^Klogseq____",1697147530467,536870922]],[logseq____"^15logseq____",[156,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[156,logseq____"^Ylogseq____",logseq____"aussagenlogseq____",536870922]],[logseq____"^15logseq____",[156,logseq____"^11logseq____",logseq____"Aussagenlogseq____",536870922]],[logseq____"^15logseq____",[156,logseq____"^Blogseq____",1697147530467,536870922]],[logseq____"^15logseq____",[156,logseq____"^;logseq____",logseq____"~u65286a8a-adf6-4703-bc93-ade55908aef4logseq____",536870922]],[logseq____"^15logseq____",[157,logseq____"^Klogseq____",1697147530472,536870922]],[logseq____"^15logseq____",[157,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[157,logseq____"^Ylogseq____",logseq____"verknüpfungenlogseq____",536870922]],[logseq____"^15logseq____",[157,logseq____"^11logseq____",logseq____"Verknüpfungenlogseq____",536870922]],[logseq____"^15logseq____",[157,logseq____"^Blogseq____",1697147530472,536870922]],[logseq____"^15logseq____",[157,logseq____"^;logseq____",logseq____"~u65286a8a-3a12-4ad9-b67f-ce39c9fe39c2logseq____",536870922]],[logseq____"^15logseq____",[158,logseq____"^Klogseq____",1697147530473,536870922]],[logseq____"^15logseq____",[158,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[158,logseq____"^Ylogseq____",logseq____"aussageformellogseq____",536870922]],[logseq____"^15logseq____",[158,logseq____"^11logseq____",logseq____"Aussageformellogseq____",536870922]],[logseq____"^15logseq____",[158,logseq____"^Blogseq____",1697147530473,536870922]],[logseq____"^15logseq____",[158,logseq____"^;logseq____",logseq____"~u65286a8a-6991-47f9-9836-402af30c00b8logseq____",536870922]],[logseq____"^15logseq____",[159,logseq____"^Klogseq____",1697147530469,536870922]],[logseq____"^15logseq____",[159,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[159,logseq____"^Ylogseq____",logseq____"syntaxlogseq____",536870922]],[logseq____"^15logseq____",[159,logseq____"^11logseq____",logseq____"Syntaxlogseq____",536870922]],[logseq____"^15logseq____",[159,logseq____"^Blogseq____",1697147530469,536870922]],[logseq____"^15logseq____",[159,logseq____"^;logseq____",logseq____"~u65286a8a-63fc-479b-8834-5cc34993e5ablogseq____",536870922]],[logseq____"^15logseq____",[160,logseq____"^Klogseq____",1697147530466,536870922]],[logseq____"^15logseq____",[160,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[160,logseq____"^Ylogseq____",logseq____"verknüpfung von aussagenlogseq____",536870922]],[logseq____"^15logseq____",[160,logseq____"^11logseq____",logseq____"Verknüpfung von Aussagenlogseq____",536870922]],[logseq____"^15logseq____",[160,logseq____"^Blogseq____",1697147530466,536870922]],[logseq____"^15logseq____",[160,logseq____"^;logseq____",logseq____"~u65286a8a-f9b1-4777-9f57-e905ff22f244logseq____",536870922]],[logseq____"^15logseq____",[161,logseq____"^Klogseq____",1697147530477,536870922]],[logseq____"^15logseq____",[161,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[161,logseq____"^Ylogseq____",logseq____"schreibweiselogseq____",536870922]],[logseq____"^15logseq____",[161,logseq____"^11logseq____",logseq____"Schreibweiselogseq____",536870922]],[logseq____"^15logseq____",[161,logseq____"^Blogseq____",1697147530477,536870922]],[logseq____"^15logseq____",[161,logseq____"^;logseq____",logseq____"~u65286a8a-089a-423b-bbde-ad9788369ccalogseq____",536870922]],[logseq____"^15logseq____",[162,logseq____"^Klogseq____",1697147530475,536870922]],[logseq____"^15logseq____",[162,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[162,logseq____"^Ylogseq____",logseq____"belegunglogseq____",536870922]],[logseq____"^15logseq____",[162,logseq____"^11logseq____",logseq____"Belegunglogseq____",536870922]],[logseq____"^15logseq____",[162,logseq____"^Blogseq____",1697147530475,536870922]],[logseq____"^15logseq____",[162,logseq____"^;logseq____",logseq____"~u65286a8a-e348-4763-b4f7-d886e97eed01logseq____",536870922]],[logseq____"^15logseq____",[163,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der Variablen)logseq____",536870922]],[logseq____"^15logseq____",[163,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[163,logseq____"^Flogseq____",184,536870922]],[logseq____"^15logseq____",[163,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[163,logseq____"^Vlogseq____",174,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[163,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[163,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[163,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[163,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[163,logseq____"^;logseq____",logseq____"~u65286a8a-c0dc-405d-af65-da7f1f73efc4logseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Qlogseq____",logseq____"[[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Flogseq____",187,536870922]],[logseq____"^15logseq____",[164,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[164,logseq____"^Vlogseq____",187,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",145,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",154,536870922]],[logseq____"^15logseq____",[164,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[164,logseq____"^;logseq____",logseq____"~u65286a8a-b4da-4e45-922f-0193216179fdlogseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Flogseq____",183,536870922]],[logseq____"^15logseq____",[165,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[165,logseq____"^Vlogseq____",141,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[165,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[165,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[165,logseq____"^Hlogseq____",156,536870922]],[logseq____"^15logseq____",[165,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[165,logseq____"^;logseq____",logseq____"~u65286a8a-49c0-4c51-a5d9-4d0e44211d27logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Flogseq____",170,536870922]],[logseq____"^15logseq____",[166,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[166,logseq____"^Vlogseq____",174,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",150,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[166,logseq____"^Hlogseq____",150,536870922]],[logseq____"^15logseq____",[166,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[166,logseq____"^;logseq____",logseq____"~u65286a8a-3e27-4f58-aef2-6b8c736b546dlogseq____",536870922]],[logseq____"^15logseq____",[167,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____",[167,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[167,logseq____"^Flogseq____",185,536870922]],[logseq____"^15logseq____",[167,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[167,logseq____"^Vlogseq____",174,536870922]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[167,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[167,logseq____"^;logseq____",logseq____"~u65286a8a-dfca-4741-aa84-8f5967065addlogseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Flogseq____",188,536870922]],[logseq____"^15logseq____",[168,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[168,logseq____"^Vlogseq____",188,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",150,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[168,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[168,logseq____"^;logseq____",logseq____"~u65286a8a-8429-47e5-93cf-7559b63f0062logseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Flogseq____",184,536870922]],[logseq____"^15logseq____",[169,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[169,logseq____"^Vlogseq____",184,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",41,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",157,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[169,logseq____"^Hlogseq____",41,536870922]],[logseq____"^15logseq____",[169,logseq____"^Hlogseq____",157,536870922]],[logseq____"^15logseq____",[169,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[169,logseq____"^;logseq____",logseq____"~u65286a8a-1c23-4e65-8426-6c0529f9a4e4logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Flogseq____",178,536870922]],[logseq____"^15logseq____",[170,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[170,logseq____"^Vlogseq____",174,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",144,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",161,536870922]],[logseq____"^15logseq____",[170,logseq____"^Hlogseq____",144,536870922]],[logseq____"^15logseq____",[170,logseq____"^Hlogseq____",153,536870922]],[logseq____"^15logseq____",[170,logseq____"^Hlogseq____",161,536870922]],[logseq____"^15logseq____",[170,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[170,logseq____"^;logseq____",logseq____"~u65286a8a-3e57-4689-9dbd-bfec45f38195logseq____",536870922]],[logseq____"^15logseq____",[171,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____",[171,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[171,logseq____"^Flogseq____",167,536870922]],[logseq____"^15logseq____",[171,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[171,logseq____"^Vlogseq____",174,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",148,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",152,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",155,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[171,logseq____"^Hlogseq____",148,536870922]],[logseq____"^15logseq____",[171,logseq____"^Hlogseq____",152,536870922]],[logseq____"^15logseq____",[171,logseq____"^Hlogseq____",155,536870922]],[logseq____"^15logseq____",[171,logseq____"^Hlogseq____",159,536870922]],[logseq____"^15logseq____",[171,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[171,logseq____"^;logseq____",logseq____"~u65286a8a-189e-4967-bb17-dcbd4a8e6517logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Flogseq____",176,536870922]],[logseq____"^15logseq____",[172,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[172,logseq____"^Vlogseq____",176,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",144,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",147,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",148,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",155,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[172,logseq____"^Hlogseq____",147,536870922]],[logseq____"^15logseq____",[172,logseq____"^Hlogseq____",148,536870922]],[logseq____"^15logseq____",[172,logseq____"^Hlogseq____",155,536870922]],[logseq____"^15logseq____",[172,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[172,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[172,logseq____"^;logseq____",logseq____"~u65286a8a-2bac-4245-a068-5a8a5fdf2adflogseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Flogseq____",178,536870922]],[logseq____"^15logseq____",[173,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[173,logseq____"^Vlogseq____",178,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",151,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[173,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[173,logseq____"^;logseq____",logseq____"~u65286a8a-3ae7-4fc2-a137-3568697275f9logseq____",536870922]],[logseq____"^15logseq____",[174,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[174,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[174,logseq____"^Flogseq____",181,536870922]],[logseq____"^15logseq____",[174,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[174,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[174,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870922]],[logseq____"^15logseq____",[174,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[174,logseq____"^Hlogseq____",160,536870922]],[logseq____"^15logseq____",[174,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[174,logseq____"^;logseq____",logseq____"~u65286a8a-c694-4fc1-a24a-f1af5234776alogseq____",536870922]],[logseq____"^15logseq____",[175,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870922]],[logseq____"^15logseq____",[175,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[175,logseq____"^Flogseq____",183,536870922]],[logseq____"^15logseq____",[175,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[175,logseq____"^Vlogseq____",183,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",149,536870922]],[logseq____"^15logseq____",[175,logseq____"^Hlogseq____",149,536870922]],[logseq____"^15logseq____",[175,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[175,logseq____"^;logseq____",logseq____"~u65286a8a-60e6-4114-9ca9-61ba47de1ce3logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Flogseq____",163,536870922]],[logseq____"^15logseq____",[176,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[176,logseq____"^Vlogseq____",174,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",144,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[176,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[176,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[176,logseq____"^Hlogseq____",144,536870922]],[logseq____"^15logseq____",[176,logseq____"^Hlogseq____",158,536870922]],[logseq____"^15logseq____",[176,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[176,logseq____"^;logseq____",logseq____"~u65286a8a-2b13-477d-8107-02a3617c7d84logseq____",536870922]],[logseq____"^15logseq____",[177,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____",[177,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[177,logseq____"^Flogseq____",166,536870922]],[logseq____"^15logseq____",[177,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[177,logseq____"^Vlogseq____",174,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[177,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[177,logseq____"^;logseq____",logseq____"~u65286a8a-32c2-491c-8044-ca1ba8eaf443logseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Flogseq____",188,536870922]],[logseq____"^15logseq____",[178,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[178,logseq____"^Vlogseq____",174,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",151,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[178,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[178,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[178,logseq____"^Hlogseq____",151,536870922]],[logseq____"^15logseq____",[178,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[178,logseq____"^;logseq____",logseq____"~u65286a8a-ed6b-4578-944b-f933ef45588dlogseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Flogseq____",163,536870922]],[logseq____"^15logseq____",[179,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[179,logseq____"^Vlogseq____",163,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[179,logseq____"^Hlogseq____",154,536870922]],[logseq____"^15logseq____",[179,logseq____"^Hlogseq____",158,536870922]],[logseq____"^15logseq____",[179,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[179,logseq____"^;logseq____",logseq____"~u65286a8a-dee3-4fa8-aa17-b421d8a28324logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Qlogseq____",logseq____"Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Flogseq____",165,536870922]],[logseq____"^15logseq____",[180,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[180,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",148,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[180,logseq____"^Hlogseq____",148,536870922]],[logseq____"^15logseq____",[180,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[180,logseq____"^;logseq____",logseq____"~u65286a8a-0c55-4e9b-8ac5-a9caeaee1f34logseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&\\logseq____"5\\\\text{ ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Flogseq____",180,536870922]],[logseq____"^15logseq____",[181,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[181,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[181,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[181,logseq____"^;logseq____",logseq____"~u65286a8a-5f1b-45ae-9e25-476514c1a637logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Flogseq____",175,536870922]],[logseq____"^15logseq____",[182,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[182,logseq____"^Vlogseq____",183,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",146,536870922]],[logseq____"^15logseq____",[182,logseq____"^Hlogseq____",146,536870922]],[logseq____"^15logseq____",[182,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[182,logseq____"^;logseq____",logseq____"~u65286a8a-cb47-43c8-ab8a-7b749f96fc16logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Flogseq____",141,536870922]],[logseq____"^15logseq____",[183,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[183,logseq____"^Vlogseq____",141,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[183,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[183,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[183,logseq____"^17logseq____",false,536870922]],[logseq____"^15logseq____",[183,logseq____"^;logseq____",logseq____"~u65286a8a-1081-44c3-bfc0-a54eade50eeflogseq____",536870922]],[logseq____"^15logseq____",[184,logseq____"^Qlogseq____",logseq____"### 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<script type="text/javascript">// Single Page Apps for GitHub Pages
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