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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____& \\\\cdots\\\\end{array}logseq____",536870919]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",90,536870919]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",90,536870919]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u65296ee7-2b39-4ff9-88e7-bd15f03b0a75logseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",55,536870919]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",55,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u65296ee7-e1f0-49bd-bf60-b5e03076f6e0logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"# [[Wurzelgleichung]]logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",104,536870919]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[54,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",30,536870919]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u65296ee7-ea60-487f-9044-f0d573590955logseq____",536870919]],[logseq____"^15logseq____",[55,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____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",49,536870919]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",67,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u65296ee7-67e0-48e8-bfff-d2a7896d6aedlogseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"\\\\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____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",72,536870919]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",72,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u65296ee7-de3c-4f54-8672-dc429820f76elogseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",61,536870919]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[57,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u65296ee7-1a21-440d-8e83-3af32f99731alogseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",67,536870919]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[58,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u65296ee7-8d5e-4114-8c43-2ade030d7652logseq____",536870919]],[logseq____"^15logseq____",[59,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____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",102,536870919]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",98,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[59,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u65296ee7-27d8-4fc8-a4dd-ac2dc20f3efblogseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[60,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[60,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",44,536870919]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",false,536870919]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u65296ee7-88bf-4bf0-b15a-073ea07c0545logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",48,536870919]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[61,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u65296ee7-10bd-476b-ba07-d7e5cc68a4c3logseq____",536870919]],[logseq____"^15logseq____",[62,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____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",104,536870919]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",104,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u65296ee7-1fd2-45fe-8250-091dec381363logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"\\\\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____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",49,536870919]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",49,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u65296ee7-816e-492f-a606-3f43e6d1d4e5logseq____",536870919]],[logseq____"^15logseq____",[64,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____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",65,536870919]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",91,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u65296ee7-822d-48d5-9e69-7e7d46205796logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",91,536870919]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",91,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",38,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",38,536870919]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u65296ee7-daee-440b-96b0-78d7c3eda216logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",60,536870919]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[66,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[66,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u65296ee7-0610-4aed-b9dc-9bab29880ae2logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",97,536870919]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[67,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u65296ee7-9009-454e-9cb5-9b5a0edc7019logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",56,536870919]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",72,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[68,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u65296ee7-5c97-4504-aeef-e538b5a435f2logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{a+5}-\\\\sqrt{x+3}logseq____&=2\\\\sqrt(x+1) 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[[Binomische Formeln]]logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",57,536870919]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[80,logseq____"^?logseq____",[logseq____"^ 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dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",48,536870919]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",48,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u65296ee7-6a6c-49b7-b722-930f7f808a7dlogseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"$\\\\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____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",92,536870919]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",78,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u65296ee7-9062-446f-b591-d9eff5e724f5logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",99,536870919]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",66,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u65296ee7-0e6b-4464-be13-abb2373e224clogseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",59,536870919]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",59,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[86,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u65296ee7-8d7d-4914-a498-356864512e8clogseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",100,536870919]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",57,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u65296ee7-ae25-4e4e-aff0-1d18af670ee3logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Qlogseq____",logseq____"$\\\\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____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",58,536870919]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",58,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[88,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u65296ee7-866f-46c2-9d7e-55fb6b96b06flogseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",60,536870919]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",60,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",46,536870919]],[logseq____"^15logseq____",[89,logseq____"^Hlogseq____",46,536870919]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u65296ee7-15f8-47f1-b7c0-4d3fd639fae7logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",96,536870919]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",80,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[90,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[90,logseq____"^Hlogseq____",28,536870919]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u65296ee7-499b-4128-9099-6f35bb1d3f57logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",72,536870919]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",90,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[91,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[91,logseq____"^Hlogseq____",32,536870919]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u65296ee7-73d5-421d-aa3d-91510e8c57a0logseq____",536870919]],[logseq____"^15logseq____",[92,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____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",78,536870919]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",78,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u65296ee7-d952-42ae-a42d-68234f5cb5aalogseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Qlogseq____",logseq____"\\\\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____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",81,536870919]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",81,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u65296ee7-992e-4ff5-9dcd-7ff049c4f53alogseq____",536870919]],[logseq____"^15logseq____",[94,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____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",61,536870919]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",61,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u65296ee7-e288-4adb-80b6-8c4fa34ab361logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",51,536870919]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",79,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[95,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u65296ee7-4832-478d-8004-c8f78b78fbdflogseq____",536870919]],[logseq____"^15logseq____",[96,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____",[96,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Flogseq____",101,536870919]],[logseq____"^15logseq____",[96,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[96,logseq____"^Vlogseq____",80,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[96,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[96,logseq____"^;logseq____",logseq____"~u65296ee7-ff0f-4315-8b88-a3171ba8f7f4logseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Flogseq____",80,536870919]],[logseq____"^15logseq____",[97,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[97,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[97,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[97,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[97,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[97,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[97,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[97,logseq____"^;logseq____",logseq____"~u65296ee7-0204-450a-a657-32fd8c90c68flogseq____",536870919]],[logseq____"^15logseq____",[98,logseq____"^Qlogseq____",logseq____"## 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style=logseq____'color: #ff0000logseq____'logseq____>MISSING 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logseq____",logseq____"^18logseq____",3],536870920]],[logseq____"^15logseq____",[121,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[121,logseq____"^Hlogseq____",107,536870920]],[logseq____"^15logseq____",[121,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[121,logseq____"^;logseq____",logseq____"~u65296ee7-86f1-48dc-aad1-612fd66b0fa0logseq____",536870920]],[logseq____"^15logseq____",[122,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1}\\\\quad 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logseq____",logseq____"^18logseq____",3],536870920]],[logseq____"^15logseq____",[125,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[125,logseq____"^Hlogseq____",107,536870920]],[logseq____"^15logseq____",[125,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[125,logseq____"^;logseq____",logseq____"~u65296ee7-01b0-4fa7-b43f-72688bc22330logseq____",536870920]],[logseq____"^15logseq____",[126,logseq____"^Qlogseq____",logseq____"Bei Multiplikation oder Division mit einem Betrag einer negativen Zahl nicht Anwendbar, da ein [[Betrag]] immer Positiv 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aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____<xlogseq____<4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes 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xlogseq____>3$\\n\\\\begin{align}\\nx+5logseq____&logseq____>0\\\\\\\\\\n|x+5|logseq____&=x+5\\\\\\\\\\nx-3logseq____&\\\\ge0\\\\\\\\\\n|x-3|logseq____&=x-3\\\\\\\\\\nx+5logseq____&logseq____<2(x-3)\\\\\\\\\\nx+5logseq____&logseq____<2x-3 logseq____&|logseq____& -2x-5\\\\\\\\\\n-xlogseq____&logseq____<-11 logseq____&|logseq____& 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Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Flogseq____",198,536870922]],[logseq____"^15logseq____",[182,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[182,logseq____"^Vlogseq____",198,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",167,536870922]],[logseq____"^15logseq____",[182,logseq____"^Hlogseq____",167,536870922]],[logseq____"^15logseq____",[182,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[182,logseq____"^;logseq____",logseq____"~u65296ee8-cc9e-4e3f-ac88-e55b94df0ad8logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\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____",[183,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Flogseq____",186,536870922]],[logseq____"^15logseq____",[183,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[183,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",166,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",171,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",173,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",177,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[183,logseq____"^Hlogseq____",166,536870922]],[logseq____"^15logseq____",[183,logseq____"^Hlogseq____",171,536870922]],[logseq____"^15logseq____",[183,logseq____"^Hlogseq____",173,536870922]],[logseq____"^15logseq____",[183,logseq____"^Hlogseq____",177,536870922]],[logseq____"^15logseq____",[183,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[183,logseq____"^;logseq____",logseq____"~u65296ee8-663b-4afc-b465-4f60ab9e6127logseq____",536870922]],[logseq____"^15logseq____",[184,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____",[184,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[184,logseq____"^Flogseq____",201,536870922]],[logseq____"^15logseq____",[184,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[184,logseq____"^Vlogseq____",201,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",166,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[184,logseq____"^Hlogseq____",166,536870922]],[logseq____"^15logseq____",[184,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[184,logseq____"^;logseq____",logseq____"~u65296ee8-5468-4b2e-a9aa-1d681fcc72bflogseq____",536870922]],[logseq____"^15logseq____",[185,logseq____"^Qlogseq____",logseq____"### [[Aussagenlogische Variable]]logseq____",536870922]],[logseq____"^15logseq____",[185,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[185,logseq____"^Flogseq____",183,536870922]],[logseq____"^15logseq____",[185,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[185,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",163,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[185,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[185,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[185,logseq____"^Hlogseq____",163,536870922]],[logseq____"^15logseq____",[185,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[185,logseq____"^;logseq____",logseq____"~u65296ee8-0f93-4c4e-989d-be5b3fe58bb3logseq____",536870922]],[logseq____"^15logseq____",[186,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[186,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[186,logseq____"^Flogseq____",192,536870922]],[logseq____"^15logseq____",[186,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[186,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[186,logseq____"^Hlogseq____",35,536870922]],[logseq____"^15logseq____",[186,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[186,logseq____"^;logseq____",logseq____"~u65296ee8-13df-4767-93f0-b0c8def37b88logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Flogseq____",196,536870922]],[logseq____"^15logseq____",[187,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[187,logseq____"^Vlogseq____",196,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",166,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",173,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[187,logseq____"^Hlogseq____",165,536870922]],[logseq____"^15logseq____",[187,logseq____"^Hlogseq____",166,536870922]],[logseq____"^15logseq____",[187,logseq____"^Hlogseq____",173,536870922]],[logseq____"^15logseq____",[187,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[187,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[187,logseq____"^;logseq____",logseq____"~u65296ee8-fa9b-4f0a-807d-8ca96335a916logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Flogseq____",190,536870922]],[logseq____"^15logseq____",[188,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[188,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",179,536870922]],[logseq____"^15logseq____",[188,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[188,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[188,logseq____"^Hlogseq____",179,536870922]],[logseq____"^15logseq____",[188,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[188,logseq____"^;logseq____",logseq____"~u65296ee8-59ce-4db2-8c05-803bfb1c086flogseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Flogseq____",206,536870922]],[logseq____"^15logseq____",[189,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[189,logseq____"^Vlogseq____",201,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[189,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870922]],[logseq____"^15logseq____",[189,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",178,536870922]],[logseq____"^15logseq____",[189,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[189,logseq____"^;logseq____",logseq____"~u65296ee8-2fe5-4afd-a9df-d240ea274d0clogseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Flogseq____",208,536870922]],[logseq____"^15logseq____",[190,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[190,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",169,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[190,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[190,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",169,536870922]],[logseq____"^15logseq____",[190,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[190,logseq____"^;logseq____",logseq____"~u65296ee8-d00c-4d70-bdf7-1316db8f0b82logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Qlogseq____",logseq____"[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Flogseq____",185,536870922]],[logseq____"^15logseq____",[191,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[191,logseq____"^Vlogseq____",185,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",163,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",170,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[191,logseq____"^Hlogseq____",170,536870922]],[logseq____"^15logseq____",[191,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[191,logseq____"^;logseq____",logseq____"~u65296ee8-bd5c-4fbb-a561-13e50d51d9f9logseq____",536870922]],[logseq____"^15logseq____",[192,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____",[192,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Flogseq____",189,536870922]],[logseq____"^15logseq____",[192,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[192,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[192,logseq____"^Hlogseq____",174,536870922]],[logseq____"^15logseq____",[192,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[192,logseq____"^;logseq____",logseq____"~u65296ee8-ac3b-4fa6-9054-ff4641340a58logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Qlogseq____",logseq____"Weitere [[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Flogseq____",202,536870922]],[logseq____"^15logseq____",[193,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[193,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[193,logseq____"^Hlogseq____",35,536870922]],[logseq____"^15logseq____",[193,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[193,logseq____"^;logseq____",logseq____"~u65296ee8-937e-47fc-83a6-6e3427e93c16logseq____",536870922]],[logseq____"^15logseq____",[194,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____",[194,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Flogseq____",187,536870922]],[logseq____"^15logseq____",[194,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[194,logseq____"^Vlogseq____",196,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[194,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[194,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[194,logseq____"^;logseq____",logseq____"~u65296ee8-fb63-43c0-aff5-36aafe108157logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der [[Variablen]])logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Flogseq____",203,536870922]],[logseq____"^15logseq____",[195,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[195,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",170,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[195,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[195,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[195,logseq____"^Hlogseq____",170,536870922]],[logseq____"^15logseq____",[195,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[195,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[195,logseq____"^;logseq____",logseq____"~u65296ee8-b0eb-472e-ad86-98f82e9e8319logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Flogseq____",195,536870922]],[logseq____"^15logseq____",[196,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[196,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",162,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[196,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[196,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",162,536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[196,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[196,logseq____"^;logseq____",logseq____"~u65296ee8-37a0-4c35-abee-db4ad264156flogseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Qlogseq____",logseq____"\\\\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____",[197,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Flogseq____",186,536870922]],[logseq____"^15logseq____",[197,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[197,logseq____"^Vlogseq____",186,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[197,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[197,logseq____"^;logseq____",logseq____"~u65296ee8-489e-4284-b9cd-2057722e6e7blogseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Flogseq____",159,536870922]],[logseq____"^15logseq____",[198,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[198,logseq____"^Vlogseq____",159,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[198,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[198,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[198,logseq____"^17logseq____",false,536870922]],[logseq____"^15logseq____",[198,logseq____"^;logseq____",logseq____"~u65296ee8-481c-4cbf-8993-1e101fadd2b3logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Flogseq____",195,536870922]],[logseq____"^15logseq____",[199,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[199,logseq____"^Vlogseq____",195,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",170,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[199,logseq____"^Hlogseq____",170,536870922]],[logseq____"^15logseq____",[199,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[199,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[199,logseq____"^;logseq____",logseq____"~u65296ee8-b4c4-492b-b71e-e872cba6c1a2logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Flogseq____",203,536870922]],[logseq____"^15logseq____",[200,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[200,logseq____"^Vlogseq____",203,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",42,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",175,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",42,536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",175,536870922]],[logseq____"^15logseq____",[200,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[200,logseq____"^;logseq____",logseq____"~u65296ee8-d516-4e66-8a14-4c4125a36e7dlogseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Flogseq____",198,536870922]],[logseq____"^15logseq____",[201,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[201,logseq____"^Vlogseq____",159,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[201,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[201,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[201,logseq____"^Hlogseq____",174,536870922]],[logseq____"^15logseq____",[201,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[201,logseq____"^;logseq____",logseq____"~u65296ee8-55d1-484c-b13e-220c9d162284logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Flogseq____",188,536870922]],[logseq____"^15logseq____",[202,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[202,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[202,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[202,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[202,logseq____"^;logseq____",logseq____"~u65296ee8-fa96-46eb-b0af-4fd95d0140d0logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Qlogseq____",logseq____"### [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Flogseq____",185,536870922]],[logseq____"^15logseq____",[203,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[203,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[203,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[203,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[203,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[203,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[203,logseq____"^;logseq____",logseq____"~u65296ee8-f6c3-45b1-a8b1-d67adbb3aa71logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Flogseq____",208,536870922]],[logseq____"^15logseq____",[204,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[204,logseq____"^Vlogseq____",208,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[204,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[204,logseq____"^;logseq____",logseq____"~u65296ee8-e000-4d90-aa38-57f6be8bbfe4logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Qlogseq____",logseq____"\\\\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____",[205,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Flogseq____",193,536870922]],[logseq____"^15logseq____",[205,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[205,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[205,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[205,logseq____"^;logseq____",logseq____"~u65296ee8-469e-4449-8475-f70ddc2aef6blogseq____",536870922]],[logseq____"^15logseq____",[206,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____",[206,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Flogseq____",184,536870922]],[logseq____"^15logseq____",[206,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[206,logseq____"^Vlogseq____",201,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[206,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[206,logseq____"^;logseq____",logseq____"~u65296ee8-72ba-44c3-9289-498e684e01ablogseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ 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[[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Flogseq____",196,536870922]],[logseq____"^15logseq____",[208,logseq____"^Xlogseq____",159,536870922]],[logseq____"^15logseq____",[208,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[208,logseq____"^?logseq____",[logseq____"^ 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morgansche regelnlogseq____",536870923]],[logseq____"^15logseq____",[211,logseq____"^11logseq____",logseq____"de Morgansche 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istlogseq____",536870923]],[logseq____"^15logseq____",[241,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[241,logseq____"^Flogseq____",248,536870923]],[logseq____"^15logseq____",[241,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[241,logseq____"^Vlogseq____",248,536870923]],[logseq____"^15logseq____",[241,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[241,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[241,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[241,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[241,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[241,logseq____"^Hlogseq____",224,536870923]],[logseq____"^15logseq____",[241,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[241,logseq____"^;logseq____",logseq____"~u65296ee8-b620-46f3-a25f-c70784b63afflogseq____",536870923]],[logseq____"^15logseq____",[242,logseq____"^Qlogseq____",logseq____"$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, logseq____",536870923]],[logseq____"^15logseq____",[242,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[242,logseq____"^Flogseq____",265,536870923]],[logseq____"^15logseq____",[242,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[242,logseq____"^Vlogseq____",265,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",212,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",215,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[242,logseq____"^Hlogseq____",212,536870923]],[logseq____"^15logseq____",[242,logseq____"^Hlogseq____",215,536870923]],[logseq____"^15logseq____",[242,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[242,logseq____"^;logseq____",logseq____"~u65296ee8-763b-4300-a34f-81dc6449ccc0logseq____",536870923]],[logseq____"^15logseq____",[243,logseq____"^Qlogseq____",logseq____"Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____",536870923]],[logseq____"^15logseq____",[243,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[243,logseq____"^Flogseq____",240,536870923]],[logseq____"^15logseq____",[243,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[243,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",210,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[243,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[243,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[243,logseq____"^;logseq____",logseq____"~u65296ee8-7ffd-4286-9346-2d05cf39e4dflogseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Qlogseq____",logseq____"see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Flogseq____",240,536870923]],[logseq____"^15logseq____",[244,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[244,logseq____"^Vlogseq____",240,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",210,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",213,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",225,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",230,536870923]],[logseq____"^15logseq____",[244,logseq____"^Hlogseq____",213,536870923]],[logseq____"^15logseq____",[244,logseq____"^Hlogseq____",225,536870923]],[logseq____"^15logseq____",[244,logseq____"^Hlogseq____",230,536870923]],[logseq____"^15logseq____",[244,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[244,logseq____"^;logseq____",logseq____"~u65296ee8-6e39-4eb3-b876-ef851e6e4eaclogseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Qlogseq____",logseq____"#FIXMElogseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Flogseq____",255,536870923]],[logseq____"^15logseq____",[245,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[245,logseq____"^Vlogseq____",255,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",42,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[245,logseq____"^Hlogseq____",42,536870923]],[logseq____"^15logseq____",[245,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[245,logseq____"^;logseq____",logseq____"~u65296ee8-41bd-41b3-b31f-10d5c770de6elogseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Flogseq____",271,536870923]],[logseq____"^15logseq____",[246,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[246,logseq____"^Vlogseq____",271,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[246,logseq____"^Hlogseq____",221,536870923]],[logseq____"^15logseq____",[246,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[246,logseq____"^;logseq____",logseq____"~u65296ee8-aeeb-4a15-acfc-6da4bb99bf98logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Qlogseq____",logseq____"Widerspruch = ↯, #logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Flogseq____",256,536870923]],[logseq____"^15logseq____",[247,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[247,logseq____"^Vlogseq____",256,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[247,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[247,logseq____"^;logseq____",logseq____"~u65296ee8-20f1-4597-9f9c-c867efe17315logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Flogseq____",272,536870923]],[logseq____"^15logseq____",[248,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[248,logseq____"^Vlogseq____",272,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[248,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[248,logseq____"^;logseq____",logseq____"~u65296ee8-251f-4afc-9532-7a7235b548d8logseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&\\\\equiv p, \\\\quad \\\\neg logseq____&\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Flogseq____",269,536870923]],[logseq____"^15logseq____",[249,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[249,logseq____"^Vlogseq____",217,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[249,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[249,logseq____"^;logseq____",logseq____"~u65296ee8-3000-4d6f-9700-9de433cbc3bdlogseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Qlogseq____",logseq____"see: [[Allquantor]] [[Existenzquantor]]logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Flogseq____",254,536870923]],[logseq____"^15logseq____",[250,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[250,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",229,536870923]],[logseq____"^15logseq____",[250,logseq____"^Hlogseq____",223,536870923]],[logseq____"^15logseq____",[250,logseq____"^Hlogseq____",229,536870923]],[logseq____"^15logseq____",[250,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[250,logseq____"^;logseq____",logseq____"~u65296ee8-ffab-40e1-bfe7-3a4a738a0bb3logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Flogseq____",248,536870923]],[logseq____"^15logseq____",[251,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[251,logseq____"^Vlogseq____",272,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[251,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[251,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[251,logseq____"^;logseq____",logseq____"~u65296ee8-e188-4f05-a878-ffc8ce0ecc6dlogseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Qlogseq____",logseq____"## [[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Flogseq____",255,536870923]],[logseq____"^15logseq____",[252,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[252,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",210,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[252,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870923]],[logseq____"^15logseq____",[252,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[252,logseq____"^Hlogseq____",210,536870923]],[logseq____"^15logseq____",[252,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[252,logseq____"^;logseq____",logseq____"~u65296ee8-8e9d-4a6a-b614-854fdd6f25bblogseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\logseq____"\\\\text{x ist prim}\\logseq____" \\\\quad logseq____& \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____"\\\\underbrace{x}_{x_1}logseq____<\\\\underbrace{y}_{x_2}\\logseq____"\\\\quad logseq____&\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____"\\\\text{x ist wahr}\\logseq____"\\\\quadlogseq____&\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Flogseq____",258,536870923]],[logseq____"^15logseq____",[253,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[253,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[253,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[253,logseq____"^;logseq____",logseq____"~u65296ee8-d1ea-4c50-93f8-c1ed42403cfflogseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Flogseq____",260,536870923]],[logseq____"^15logseq____",[254,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[254,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[254,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[254,logseq____"^;logseq____",logseq____"~u65296ee8-66ea-4bd8-bfad-32efbdbd2dfdlogseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Qlogseq____",logseq____"Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Flogseq____",236,536870923]],[logseq____"^15logseq____",[255,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[255,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[255,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[255,logseq____"^;logseq____",logseq____"~u65296ee8-71cd-4ff9-9190-ab6d0b256235logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Qlogseq____",logseq____"Wäre $y$ aus $\\\\Reals$ mit $xlogseq____<y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____<y$, Widerspruch. $\\\\blacksquare$logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Flogseq____",268,536870923]],[logseq____"^15logseq____",[256,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[256,logseq____"^Vlogseq____",268,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[256,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[256,logseq____"^;logseq____",logseq____"~u65296ee8-3cce-471a-b540-e06632af45b5logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Qlogseq____",logseq____"$\\\\forall x:p(x)$ ist die [Aussage]([[[]Aussagen]]): $\\logseq____"\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____"\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Flogseq____",259,536870923]],[logseq____"^15logseq____",[257,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[257,logseq____"^Vlogseq____",259,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",166,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",235,536870923]],[logseq____"^15logseq____",[257,logseq____"^Hlogseq____",166,536870923]],[logseq____"^15logseq____",[257,logseq____"^Hlogseq____",235,536870923]],[logseq____"^15logseq____",[257,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[257,logseq____"^;logseq____",logseq____"~u65296ee8-c453-4054-b529-083ac106834blogseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Flogseq____",270,536870923]],[logseq____"^15logseq____",[258,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[258,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[258,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[258,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[258,logseq____"^;logseq____",logseq____"~u65296ee8-5283-419e-8bfb-1f078655710alogseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Qlogseq____",logseq____"Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Flogseq____",253,536870923]],[logseq____"^15logseq____",[259,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[259,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[259,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[259,logseq____"^;logseq____",logseq____"~u65296ee8-e1bf-4638-a03e-2bd48bac1cb8logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Qlogseq____",logseq____"Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Flogseq____",264,536870923]],[logseq____"^15logseq____",[260,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[260,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[260,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[260,logseq____"^;logseq____",logseq____"~u65296ee8-dbf4-4e48-8c71-26f593e423aalogseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Flogseq____",272,536870923]],[logseq____"^15logseq____",[261,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[261,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[261,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[261,logseq____"^;logseq____",logseq____"~u65296ee8-c07d-427b-907b-4476304d19b0logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Qlogseq____",logseq____"[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Flogseq____",237,536870923]],[logseq____"^15logseq____",[262,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[262,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",232,536870923]],[logseq____"^15logseq____",[262,logseq____"^Hlogseq____",228,536870923]],[logseq____"^15logseq____",[262,logseq____"^Hlogseq____",232,536870923]],[logseq____"^15logseq____",[262,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[262,logseq____"^;logseq____",logseq____"~u65296ee8-6ebf-4e8e-b037-9e7844650bb1logseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Qlogseq____",logseq____"Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Flogseq____",241,536870923]],[logseq____"^15logseq____",[263,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[263,logseq____"^Vlogseq____",248,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[263,logseq____"^Hlogseq____",222,536870923]],[logseq____"^15logseq____",[263,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[263,logseq____"^;logseq____",logseq____"~u65296ee8-bf0b-4f79-9d44-07e4092b7302logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Qlogseq____",logseq____"Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Flogseq____",273,536870923]],[logseq____"^15logseq____",[264,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[264,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[264,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[264,logseq____"^;logseq____",logseq____"~u65296ee8-5fbe-4a13-a1f0-dd7444bb6a05logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Qlogseq____",logseq____"Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____<x+1=y$ also $xlogseq____<y$. $\\\\blacksquare$logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Flogseq____",246,536870923]],[logseq____"^15logseq____",[265,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[265,logseq____"^Vlogseq____",246,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",221,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[265,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[265,logseq____"^;logseq____",logseq____"~u65296ee8-4ddc-497b-93b7-2f7775e34e3clogseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Qlogseq____",logseq____"Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Flogseq____",243,536870923]],[logseq____"^15logseq____",[266,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[266,logseq____"^Vlogseq____",243,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",210,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[266,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[266,logseq____"^;logseq____",logseq____"~u65296ee8-4f92-4807-95ca-fa86e3bd49c1logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Qlogseq____",logseq____"Nach Ersetzung von $x$ in der AF $\\logseq____"xlogseq____<y\\logseq____"$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____"17logseq____<y\\logseq____"$logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Flogseq____",253,536870923]],[logseq____"^15logseq____",[267,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[267,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[267,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[267,logseq____"^;logseq____",logseq____"~u65296ee8-2669-447a-927d-7ae3e0aefb3flogseq____",536870923]],[logseq____"^15logseq____",[268,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist 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[[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Flogseq____",217,536870923]],[logseq____"^15logseq____",[269,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[269,logseq____"^Vlogseq____",217,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",210,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[269,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[269,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",210,536870923]],[logseq____"^15logseq____",[269,logseq____"^17logseq____",false,536870923]],[logseq____"^15logseq____",[269,logseq____"^;logseq____",logseq____"~u65296ee8-6b47-4753-a737-e90ef29498dclogseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Qlogseq____",logseq____"[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Flogseq____",262,536870923]],[logseq____"^15logseq____",[270,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[270,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",170,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",174,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",231,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[270,logseq____"^Hlogseq____",170,536870923]],[logseq____"^15logseq____",[270,logseq____"^Hlogseq____",174,536870923]],[logseq____"^15logseq____",[270,logseq____"^Hlogseq____",231,536870923]],[logseq____"^15logseq____",[270,logseq____"^Hlogseq____",234,536870923]],[logseq____"^15logseq____",[270,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[270,logseq____"^;logseq____",logseq____"~u65296ee8-fa2b-4990-9670-05ac999aa62elogseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Qlogseq____",logseq____"Betrachte $\\logseq____"xlogseq____<y\\logseq____"$ als AF über $\\\\Reals, \\\\Reals$logseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Flogseq____",251,536870923]],[logseq____"^15logseq____",[271,logseq____"^Xlogseq____",217,536870923]],[logseq____"^15logseq____",[271,logseq____"^Vlogseq____",251,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",218,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[271,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[271,logseq____"^;logseq____",logseq____"~u65296ee8-d739-4abb-8ae2-87f74ae51581logseq____",536870923]],[logseq____"^15logseq____",[272,logseq____"^Qlogseq____",logseq____"[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht 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beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der 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