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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____& 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ergibtlogseq____",536870919]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",92,536870919]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",92,536870919]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[51,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u6526ec23-e350-4709-831c-2eb58971d661logseq____",536870919]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870919]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",55,536870919]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",55,536870919]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[52,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u6526ec23-318d-422a-9729-67ff9c824fd2logseq____",536870919]],[logseq____"^15logseq____",[53,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____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",92,536870919]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u6526ec23-0797-40a1-800f-b653c4ae337dlogseq____",536870919]],[logseq____"^15logseq____",[54,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____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",90,536870919]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",58,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u6526ec23-cde9-4bda-8988-9df4ca5d0495logseq____",536870919]],[logseq____"^15logseq____",[55,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____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",46,536870919]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",57,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u6526ec23-4694-425b-861f-a784210d3f5clogseq____",536870919]],[logseq____"^15logseq____",[56,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____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",77,536870919]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",97,536870919]],[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____",42,536870919]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6526ec23-d503-41e2-98ee-59396983a16dlogseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",82,536870919]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[57,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[57,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u6526ec23-3355-420d-805f-86b274953fd8logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",57,536870919]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[58,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[58,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",34,536870919]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u6526ec23-0ddd-4032-a35f-55e3cb878e21logseq____",536870919]],[logseq____"^15logseq____",[59,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____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",64,536870919]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",96,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u6526ec23-b54f-4490-832f-055c54900a65logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",87,536870919]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",65,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[60,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[60,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",29,536870919]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6526ec23-894e-4656-b7b3-4ec3d81a8ad1logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&, a,b,logseq____>0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",76,536870919]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",81,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",38,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u6526ec23-859f-47ff-8d58-469d12bb6abelogseq____",536870919]],[logseq____"^15logseq____",[62,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____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",80,536870919]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",80,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u6526ec23-60c7-4496-a9a0-066d910949a2logseq____",536870919]],[logseq____"^15logseq____",[63,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____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",60,536870919]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",60,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6526ec23-bee1-47b7-b6d2-6e9859019bdblogseq____",536870919]],[logseq____"^15logseq____",[64,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____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",75,536870919]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",96,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u6526ec23-c1bf-4054-b718-3958c6b48e63logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",58,536870919]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[65,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[65,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6526ec23-adb0-4467-a95e-af18073cc4c5logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",59,536870919]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",59,536870919]],[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____"~u6526ec23-170d-4108-a5d9-a0bcbca660f3logseq____",536870919]],[logseq____"^15logseq____",[67,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____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",49,536870919]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",50,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u6526ec23-2a85-4511-bc43-ed84c98c0f7elogseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",80,536870919]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[68,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[68,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[68,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u6526ec23-3f21-4d8b-aa80-ad4cf87c49ealogseq____",536870919]],[logseq____"^15logseq____",[69,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____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",87,536870919]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[69,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u6526ec23-554a-408a-b6d4-6fff227b9371logseq____",536870919]],[logseq____"^15logseq____",[70,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____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",73,536870919]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",68,536870919]],[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____"~u6526ec23-4002-47e3-aa4a-dbd81cf90758logseq____",536870919]],[logseq____"^15logseq____",[71,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____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",69,536870919]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",27,536870919]],[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____"~u6526ec23-34da-424b-a346-7cea6b4884e8logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",74,536870919]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[72,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[72,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[72,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u6526ec23-225d-4344-8bd5-4424f5d64879logseq____",536870919]],[logseq____"^15logseq____",[73,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____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",68,536870919]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",68,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u6526ec23-67ef-445a-80b1-7e6ea9a4c00alogseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",39,536870919]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[74,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[74,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",43,536870919]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",false,536870919]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u6526ec23-0fd4-4e46-8df1-992f5d8a970alogseq____",536870919]],[logseq____"^15logseq____",[75,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____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",96,536870919]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",96,536870919]],[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____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u6526ec23-33f2-4ac1-a7d9-ffa274e605eblogseq____",536870919]],[logseq____"^15logseq____",[76,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____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",81,536870919]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",81,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",38,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u6526ec23-c704-46f4-9db8-cd68341f95d4logseq____",536870919]],[logseq____"^15logseq____",[77,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____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",93,536870919]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[77,logseq____"^Hlogseq____",40,536870919]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u6526ec23-7d3a-4cce-aaa8-cb99bc7304aclogseq____",536870919]],[logseq____"^15logseq____",[78,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____",[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____",77,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u6526ec23-e602-48d8-b947-75cef0f8e704logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",48,536870919]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",72,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u6526ec23-7d65-4b36-ac27-1b8145128333logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",72,536870919]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[80,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[80,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[80,logseq____"^Hlogseq____",31,536870919]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u6526ec23-84c3-422e-ba79-839393942486logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",53,536870919]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",38,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[81,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[81,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[81,logseq____"^Hlogseq____",38,536870919]],[logseq____"^15logseq____",[81,logseq____"^Hlogseq____",44,536870919]],[logseq____"^15logseq____",[81,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u6526ec23-2c59-4807-9bdb-33ba22710b7alogseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[82,logseq____"^Flogseq____",68,536870919]],[logseq____"^15logseq____",[82,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[82,logseq____"^Vlogseq____",39,536870919]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[82,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[82,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[82,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u6526ec23-9f63-4e6e-aac7-7d03a645e133logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{a+5}-\\\\sqrt{x+3}logseq____&=2\\\\sqrt(x+1) logseq____&|logseq____&()^2\\\\\\\\\\n\\\\left(\\\\sqrt{x+5}-\\\\sqrt{x+3}\\\\right)^2logseq____&=4(x+1)\\\\\\\\\\n(x+5)-2\\\\sqrt{x+5}\\\\sqrt{x+3}+(x+3)logseq____&=4x+4logseq____&|logseq____&-(2x+8)\\\\\\\\\\n-2\\\\sqrt{(x+5)(x+3)}logseq____&=2x-4 logseq____&|logseq____&()^2\\\\\\\\\\n4(x+5)(x+3)logseq____&=4x^2-16x+16\\\\\\\\\\n4x^2+32x+60logseq____&=4x^2-16x+16logseq____&|logseq____&-4x^2+16x-16\\\\\\\\\\n48x+44logseq____&=0\\\\quad x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",47,536870919]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",47,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",30,536870919]],[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____"~u6526ec23-f4f0-456c-9966-87a515706f11logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",74,536870919]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",74,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",45,536870919]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u6526ec23-3c51-4aad-bf70-496ba22fd160logseq____",536870919]],[logseq____"^15logseq____",[85,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____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",95,536870919]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",86,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u6526ec23-b95a-4081-bbf0-4024cb1f05b4logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",67,536870919]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",50,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[86,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[86,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[86,logseq____"^Hlogseq____",32,536870919]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u6526ec23-338b-4489-8bde-8c7c3b021701logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",96,536870919]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",65,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",27,536870919]],[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____",36,536870919]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u6526ec23-b3dd-472c-bfa0-7d823c72aec1logseq____",536870919]],[logseq____"^15logseq____",[88,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____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",62,536870919]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",80,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u6526ec23-c800-47e6-9dee-a7f4a48895a1logseq____",536870919]],[logseq____"^15logseq____",[89,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____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",82,536870919]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",82,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u6526ec23-7c8f-427a-bb6f-35bb5faec179logseq____",536870919]],[logseq____"^15logseq____",[90,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____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",58,536870919]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",58,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u6526ec23-8a86-4bde-b083-d336ad10b9b3logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",67,536870919]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",67,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[91,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u6526ec23-6350-4f54-beb9-e01fd626fc5clogseq____",536870919]],[logseq____"^15logseq____",[92,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____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",71,536870919]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",87,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u6526ec23-5aaa-4844-b0c2-ed3f864381aflogseq____",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____",97,536870919]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",97,536870919]],[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____"~u6526ec23-eda0-4064-9d18-4ef63dd758c5logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"https://www.wolframalpha.comlogseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",84,536870919]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",84,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u6526ec23-6e51-43a8-b97a-06efa78925a5logseq____",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____",86,536870919]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",39,536870919]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",86,536870919]],[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____"~u6526ec23-46ce-4f82-840c-e9a13d84260elogseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Qlogseq____",logseq____"# 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äquivalentlogseq____",536870922]],[logseq____"^15logseq____",[153,logseq____"^Blogseq____",1697049636478,536870922]],[logseq____"^15logseq____",[153,logseq____"^;logseq____",logseq____"~u6526ec24-2740-448c-b8d4-a5db8b520662logseq____",536870922]],[logseq____"^15logseq____",[154,logseq____"^Klogseq____",1697049636471,536870922]],[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____",1697049636471,536870922]],[logseq____"^15logseq____",[154,logseq____"^;logseq____",logseq____"~u6526ec24-a705-45f9-936e-da6b3d37a08flogseq____",536870922]],[logseq____"^15logseq____",[155,logseq____"^Klogseq____",1697049636472,536870922]],[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____",1697049636472,536870922]],[logseq____"^15logseq____",[155,logseq____"^;logseq____",logseq____"~u6526ec24-535f-41d0-9ca0-eeda40404618logseq____",536870922]],[logseq____"^15logseq____",[156,logseq____"^Klogseq____",1697049636462,536870922]],[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____",1697049636462,536870922]],[logseq____"^15logseq____",[156,logseq____"^;logseq____",logseq____"~u6526ec24-a347-4086-b4df-904f8f7465e8logseq____",536870922]],[logseq____"^15logseq____",[157,logseq____"^Klogseq____",1697049636470,536870922]],[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____",1697049636470,536870922]],[logseq____"^15logseq____",[157,logseq____"^;logseq____",logseq____"~u6526ec24-8049-479c-935c-1b5f44a80f52logseq____",536870922]],[logseq____"^15logseq____",[158,logseq____"^Klogseq____",1697049636471,536870922]],[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____",1697049636471,536870922]],[logseq____"^15logseq____",[158,logseq____"^;logseq____",logseq____"~u6526ec24-fa45-48cf-b220-fa44b1c58a3dlogseq____",536870922]],[logseq____"^15logseq____",[159,logseq____"^Klogseq____",1697049636465,536870922]],[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____",1697049636465,536870922]],[logseq____"^15logseq____",[159,logseq____"^;logseq____",logseq____"~u6526ec24-b44b-40f3-a445-a23d48b5c212logseq____",536870922]],[logseq____"^15logseq____",[160,logseq____"^Klogseq____",1697049636461,536870922]],[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____",1697049636461,536870922]],[logseq____"^15logseq____",[160,logseq____"^;logseq____",logseq____"~u6526ec24-682f-4728-8f5d-e2748021197alogseq____",536870922]],[logseq____"^15logseq____",[161,logseq____"^Klogseq____",1697049636477,536870922]],[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____",1697049636477,536870922]],[logseq____"^15logseq____",[161,logseq____"^;logseq____",logseq____"~u6526ec24-ca79-45c3-b0ba-69e616a19089logseq____",536870922]],[logseq____"^15logseq____",[162,logseq____"^Klogseq____",1697049636473,536870922]],[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____",1697049636473,536870922]],[logseq____"^15logseq____",[162,logseq____"^;logseq____",logseq____"~u6526ec24-76f0-40a5-87e2-2a960e5c3cfclogseq____",536870922]],[logseq____"^15logseq____",[163,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____",[163,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[163,logseq____"^Flogseq____",170,536870922]],[logseq____"^15logseq____",[163,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[163,logseq____"^Vlogseq____",170,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",148,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[163,logseq____"^Hlogseq____",148,536870922]],[logseq____"^15logseq____",[163,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[163,logseq____"^;logseq____",logseq____"~u6526ec24-3201-4864-bc30-f2dc94aa9108logseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Qlogseq____",logseq____"### [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Flogseq____",184,536870922]],[logseq____"^15logseq____",[164,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[164,logseq____"^Vlogseq____",168,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",150,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[164,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[164,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",150,536870922]],[logseq____"^15logseq____",[164,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[164,logseq____"^;logseq____",logseq____"~u6526ec24-361e-418f-878c-5aa9b9e22f94logseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Flogseq____",180,536870922]],[logseq____"^15logseq____",[165,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[165,logseq____"^Vlogseq____",168,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",150,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[165,logseq____"^Hlogseq____",150,536870922]],[logseq____"^15logseq____",[165,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[165,logseq____"^;logseq____",logseq____"~u6526ec24-b495-40c9-8d24-d446c16130d6logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Flogseq____",184,536870922]],[logseq____"^15logseq____",[166,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[166,logseq____"^Vlogseq____",184,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",144,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",147,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",148,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",155,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[166,logseq____"^Hlogseq____",147,536870922]],[logseq____"^15logseq____",[166,logseq____"^Hlogseq____",148,536870922]],[logseq____"^15logseq____",[166,logseq____"^Hlogseq____",155,536870922]],[logseq____"^15logseq____",[166,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[166,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[166,logseq____"^;logseq____",logseq____"~u6526ec24-2ac5-4e2f-b3d8-92442668ad11logseq____",536870922]],[logseq____"^15logseq____",[167,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____",[167,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[167,logseq____"^Flogseq____",168,536870922]],[logseq____"^15logseq____",[167,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[167,logseq____"^Vlogseq____",168,536870922]],[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____"^Hlogseq____",156,536870922]],[logseq____"^15logseq____",[167,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[167,logseq____"^;logseq____",logseq____"~u6526ec24-417b-42dd-805a-7796bc87862alogseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Flogseq____",185,536870922]],[logseq____"^15logseq____",[168,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[168,logseq____"^Vlogseq____",170,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[168,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870922]],[logseq____"^15logseq____",[168,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[168,logseq____"^Hlogseq____",160,536870922]],[logseq____"^15logseq____",[168,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[168,logseq____"^;logseq____",logseq____"~u6526ec24-dc05-4146-9774-5526ddcef24clogseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Qlogseq____",logseq____"### [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Flogseq____",176,536870922]],[logseq____"^15logseq____",[169,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[169,logseq____"^Vlogseq____",168,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[169,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[169,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[169,logseq____"^Hlogseq____",158,536870922]],[logseq____"^15logseq____",[169,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[169,logseq____"^;logseq____",logseq____"~u6526ec24-9ff8-432f-93b1-933c2287c074logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Flogseq____",171,536870922]],[logseq____"^15logseq____",[170,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[170,logseq____"^Vlogseq____",141,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[170,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[170,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[170,logseq____"^Hlogseq____",156,536870922]],[logseq____"^15logseq____",[170,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[170,logseq____"^;logseq____",logseq____"~u6526ec24-9e73-4802-b3c6-552aed5ceda3logseq____",536870922]],[logseq____"^15logseq____",[171,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870922]],[logseq____"^15logseq____",[171,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[171,logseq____"^Flogseq____",141,536870922]],[logseq____"^15logseq____",[171,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[171,logseq____"^Vlogseq____",141,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[171,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[171,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[171,logseq____"^17logseq____",false,536870922]],[logseq____"^15logseq____",[171,logseq____"^;logseq____",logseq____"~u6526ec24-5732-447b-96e3-71a52151c693logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Flogseq____",164,536870922]],[logseq____"^15logseq____",[172,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[172,logseq____"^Vlogseq____",168,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",151,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[172,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[172,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[172,logseq____"^Hlogseq____",151,536870922]],[logseq____"^15logseq____",[172,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[172,logseq____"^;logseq____",logseq____"~u6526ec24-9c71-42f3-9e2c-f12fbbf993f7logseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Flogseq____",183,536870922]],[logseq____"^15logseq____",[173,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[173,logseq____"^Vlogseq____",171,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",146,536870922]],[logseq____"^15logseq____",[173,logseq____"^Hlogseq____",146,536870922]],[logseq____"^15logseq____",[173,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[173,logseq____"^;logseq____",logseq____"~u6526ec24-90af-4f29-9de8-7e029ed9daf5logseq____",536870922]],[logseq____"^15logseq____",[174,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____",[174,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[174,logseq____"^Flogseq____",167,536870922]],[logseq____"^15logseq____",[174,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[174,logseq____"^Vlogseq____",168,536870922]],[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____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[174,logseq____"^;logseq____",logseq____"~u6526ec24-cfca-43f7-8913-17001f4ba1eclogseq____",536870922]],[logseq____"^15logseq____",[175,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____",[175,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[175,logseq____"^Flogseq____",174,536870922]],[logseq____"^15logseq____",[175,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[175,logseq____"^Vlogseq____",168,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",148,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",152,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",155,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[175,logseq____"^Hlogseq____",148,536870922]],[logseq____"^15logseq____",[175,logseq____"^Hlogseq____",152,536870922]],[logseq____"^15logseq____",[175,logseq____"^Hlogseq____",155,536870922]],[logseq____"^15logseq____",[175,logseq____"^Hlogseq____",159,536870922]],[logseq____"^15logseq____",[175,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[175,logseq____"^;logseq____",logseq____"~u6526ec24-9475-4729-9b1e-6cccb7acb685logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Qlogseq____",logseq____"### [[Aussagenlogische Variable]]logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Flogseq____",175,536870922]],[logseq____"^15logseq____",[176,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[176,logseq____"^Vlogseq____",168,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",145,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",156,536870922]],[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____",145,536870922]],[logseq____"^15logseq____",[176,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[176,logseq____"^;logseq____",logseq____"~u6526ec24-a2a3-49fc-9239-c74087347edelogseq____",536870922]],[logseq____"^15logseq____",[177,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870922]],[logseq____"^15logseq____",[177,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[177,logseq____"^Flogseq____",172,536870922]],[logseq____"^15logseq____",[177,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[177,logseq____"^Vlogseq____",172,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",151,536870922]],[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____"~u6526ec24-b10a-4cc8-8b91-f56fc18c3881logseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Flogseq____",166,536870922]],[logseq____"^15logseq____",[178,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[178,logseq____"^Vlogseq____",184,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",144,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[178,logseq____"^Hlogseq____",144,536870922]],[logseq____"^15logseq____",[178,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[178,logseq____"^;logseq____",logseq____"~u6526ec24-a450-4ec2-a4d0-2c6361b94e56logseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Flogseq____",169,536870922]],[logseq____"^15logseq____",[179,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[179,logseq____"^Vlogseq____",169,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",41,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",157,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[179,logseq____"^Hlogseq____",41,536870922]],[logseq____"^15logseq____",[179,logseq____"^Hlogseq____",157,536870922]],[logseq____"^15logseq____",[179,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[179,logseq____"^;logseq____",logseq____"~u6526ec24-284f-4642-84e6-18ea782882d2logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Flogseq____",172,536870922]],[logseq____"^15logseq____",[180,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[180,logseq____"^Vlogseq____",168,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",144,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",161,536870922]],[logseq____"^15logseq____",[180,logseq____"^Hlogseq____",144,536870922]],[logseq____"^15logseq____",[180,logseq____"^Hlogseq____",153,536870922]],[logseq____"^15logseq____",[180,logseq____"^Hlogseq____",161,536870922]],[logseq____"^15logseq____",[180,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[180,logseq____"^;logseq____",logseq____"~u6526ec24-fd02-40cb-bf4a-30d7f99254e4logseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Qlogseq____",logseq____"[[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Flogseq____",176,536870922]],[logseq____"^15logseq____",[181,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[181,logseq____"^Vlogseq____",176,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",145,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[181,logseq____"^Hlogseq____",154,536870922]],[logseq____"^15logseq____",[181,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[181,logseq____"^;logseq____",logseq____"~u6526ec24-1017-425e-95c0-fd12ed8df061logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Flogseq____",164,536870922]],[logseq____"^15logseq____",[182,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[182,logseq____"^Vlogseq____",164,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",150,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[182,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[182,logseq____"^;logseq____",logseq____"~u6526ec24-294d-437a-9f58-406242aa9452logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Flogseq____",171,536870922]],[logseq____"^15logseq____",[183,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[183,logseq____"^Vlogseq____",171,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",149,536870922]],[logseq____"^15logseq____",[183,logseq____"^Hlogseq____",149,536870922]],[logseq____"^15logseq____",[183,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[183,logseq____"^;logseq____",logseq____"~u6526ec24-1978-418f-bf9d-561bf4df0c6flogseq____",536870922]],[logseq____"^15logseq____",[184,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[184,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[184,logseq____"^Flogseq____",186,536870922]],[logseq____"^15logseq____",[184,logseq____"^Xlogseq____",141,536870922]],[logseq____"^15logseq____",[184,logseq____"^Vlogseq____",168,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",144,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",160,536870922]],[logseq____"^15logseq____",[184,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[184,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[184,logseq____"^Hlogseq____",144,536870922]],[logseq____"^15logseq____",[184,logseq____"^Hlogseq____",158,536870922]],[logseq____"^15logseq____",[184,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[184,logseq____"^;logseq____",logseq____"~u6526ec24-e569-49fb-9812-f89602215487logseq____",536870922]],[logseq____"^15logseq____",[185,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 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