Definición:
f(a) = b <==> a =[m]= b
Teorema:
Sea a =[2]= 0 ==>
x^{2}+ax =[2]= p <==> x =[2]= p
x = 2k & p = 2j
x = 2k+1 & p = 2j+1
Demostración:
a =[2]= 0
f(a) = 0
x+ax =[2]= x^{2}+ax =[2]= p
f(x) = f(x)+f(a)·f(x) = f(x+ax) = p
x =[2]= p
Teorema:
Sea a =[2]= 1 ==>
x^{2}+ax+(-1) =[2]= p <==> x =[2]= p
x = 2k+1 & p = 2j+1
Demostración:
a =[2]= 1
f(a) = 1
ax =[2]= 1+ax+(-1) =[2]= x^{2}+ax+(-1) =[2]= p
f(x) = f(a)·f(x) = f(ax) = p
x =[2]= p
Teorema:
Sea a =[2]= 1 ==>
x^{2}+ax =[2]= p <==> 2x =[2]= p
x = 2k & p = 4j
x = 2k+1 & p = 4j+2
Demostración:
a =[2]= 1
f(a) = 1
x+ax =[2]= x^{2}+ax =[2]= p
f(2x) = f(x)+f(x) =f(x)+f(a)·f(x) = f(x+ax) = p
2x =[2]= p
Anexo:
k = 1 & j = 4
9+3·3 = 18 = 4·4+2
k = 2 & j = 7
16+4·3 = 28 = 4·7
Topología cociente:
< A [&] ¬B , A [ || ] ¬B > € VxV || < ¬A [ || ] B , ¬A [&] B > € VxV
Teorema
< A [&] ¬A , A [ || ] ¬A > = < 0 , E > € VxV
< ¬A [ || ] A , ¬A [&] A > = < E , 0 > € VxV
Teorema:
< A [&] ¬B , A [ || ] ¬B > € VxV
<==>
< ¬A [ || ] B , ¬A [&] B > € VxV
Teorema:
Si < (A [&] ¬B) [ || ] (B [&] ¬C), (A [ || ] ¬B) [&] (B [ || ] ¬C) > € VxV ==> ...
... < A [&] ¬C , A [ || ] ¬C > € VxV
Si < (¬A [ || ] B) [&] (¬B [ || ] C), (¬A [&] B) [ || ] (¬B [&] C) > € VxV ==> ...
... < ¬A [ || ] C , ¬A [&] C > € VxV
Teorema:
¬( < 1,0 > ) = < 1+(-1),1+(-0) > = < 0,1 >
¬( < (1/3),(2/3) > ) = < 1+(-1)·(1/3),1+(-1)·(2/3) > = < (2/3),(1/3) >
Teorema:
int[x = 0]-[1][ e^{x}·cos(x^{(1/2)}) ]d[x] = 1+(-1)·sum[k = 0]-[oo][ (-1)^{k}·(1/(2k+1)!)·e ]
Demostración:
x = y^{2} & d[x] = 2y·d[y]
int[ e^{x}·cos(x^{(1/2)}) ]d[x] = int[ 2ye^{y^{2}}·cos(y) ]d[y] = e^{y^{2}} [o(y)o] sin(y)
(0/0) = ((-0)/0) = (-1)
( 1^{(1/2)} )^{2k+1} = (-1)^{2k+1} = (-1)·(-1)^{2k} = (-1)
Teorema:
int[x = 0]-[1][ e^{x}·sin(x^{(1/2)}) ]d[x] = 1+(-1)·sum[k = 0]-[oo][ (-1)^{k}·(1/(2k)!)·e ]
Demostración:
x = y^{2} & d[x] = 2y·d[y]
int[ e^{x}·sin(x^{(1/2)}) ]d[x] = int[ 2ye^{y^{2}}·sin(y) ]d[y] = e^{y^{2}} [o(y)o] (-1)·cos(y)
Si conocéis a alguien que es,
el Mal no vos a va a decir que la gente es,
porque es la negación de cuando no conocéis,
o no hay ninguien que sea,
en vuestra vida.
