economía

Lema:

p = 1·100+(1/1)·1,000 = 1,100€

q = 10·100+(1/10)·1,000 = 1,100€

Lema:

p = 2·100+(1/2)·1,000 = 700€

q = 5·100+(1/5)·1,000 = 700€

Lema:

p = 10^{1}+1,000^{(1/1)} = 1,010€

q = 10^{3}+1,000^{(1/3)} = 1,010€

Lema:

p = 50^{1}+2,500^{(1/1)} = 2,550€

q = 50^{2}+2,500^{(1/2)} = 2,550€

Impuesto de 1€ por unidades del producto

Lema:

(nx)^{p} = x^{p} <==> n = 1€

((1/n)·x)^{p} = x^{p} <==> n = 1€

Disertación:

(nx)^{p} = x^{p}

p·ln(nx) = p·ln(x)

ln(nx) = ln(x)

e^{ln(nx)} = e^{ln(x)}

nx = x

n = 1

Lema:

e^{nx} = e^{x} <==> n = 1€

e^{(1/n)·x} = e^{x} <==> n = 1€

Disertación:

e^{nx} = e^{x}

nx·ln(e) = x·ln(e)

nx = x

n = 1

Lema:

ln(nx) = ln(x) <==> n = 1€

ln((1/n)·x) = ln(x) <==> n = 1€

Disertación:

ln(nx) = ln(x)

e^{ln(nx)} = e^{ln(x)}

nx = x

n = 1

Lema:

(nx)^{p}·e^{nx} = x^{p}·e^{x} <==> n = 1€

((1/n)·x)^{p}·e^{(1/n)·x} = x^{p}·e^{x} <==> n = 1€

Disertación:

(nx)^{p}·e^{nx} = x^{p}·e^{x}

Anti-[ s^{p}·e^{s} ]-( (nx)^{p}·e^{nx} ) = Anti-[ s^{p}·e^{s} ]-( x^{p}·e^{x} )

nx = x

n = 1

Lema:

(nx)^{p}·ln(nx) = x^{p}·ln(x) <==> n = 1€

((1/n)·x)^{p}·ln((1/n)·x) = x^{p}·ln(x) <==> n = 1€

Disertación:

(nx)^{p}·ln(nx) = x^{p}·ln(x)

Anti-[ s^{p}·ln(s) ]-( (nx)^{p}·ln(nx) ) = Anti-[ s^{p}·ln(s) ]-( x^{p}·ln(x) )

nx = x

n = 1

Ley:

Después de la resurrección de los muertos,

se pueden recordar algo dual,

siendo 0t < (1/2)

Después de la resurrección de los muertos,

no se pueden recordar nada no dual,

siendo 0t > (0/2)

Ley:

Después de la resurrección de los muertos,

se pueden recordar teoremas,

siendo 0t < 1

Después de la resurrección de los muertos,

no se pueden recordar artes destructores,

siendo 0t > (-1)

Que están en una guerra contra los hombres,

y que son maricones,

no se lo cree ninguien,

en ser una falsedad,

y llegar los hombres,

a la resurrección de los muertos.

mecanismo-de-Gauge y álgebra y análisis-matemático y filosofía y geometría-diferencial y homología-algebraica y topología

Ley:

Sea m·d_{tt}^{2}[z] = pE_{e}(z,q) ==>

Si q = 0 ==> p = m

Ley:

Sea m·d_{tt}^{2}[z] = pE_{g}(z,q) ==>

Si q = 0 ==> p = m

Electro-débil de leptones orbitales:

Ley:

F(t)·G(t) = e^{(1/m)·(q+(-W))}·e^{(1/m)·(W+(-q))}·f(t)·g(t)

d_{t}[F(t)]·d_{t}[G(t)] = ...

... d_{t}[f(t)]·d_{t}[g(t)]+(1/m)^{2}·d_{t}[q+(-W)]·d_{t}[W+(-q)]·f(t)·g(t)

Ley:

Sea A(x,y) = (1/m)·< x,y > ==>

F(x,y)·G(x,y) = e^{ Anti-Potencial[ A(x,y)·a^{2}·< q+(-W),W+(-q) > ] }·f(x,y)·g(x,y)

d_{y}[F(x,y)]·d_{x}[G(x,y)] = ...

... d_{y}[f(x,y)]·d_{x}[g(x,y)]+( A_{x}·A_{y} )·a^{4}·(q+(-W))·(W+(-q))·f(x,y)·g(x,y)

Deducción:

F(x,y) = e^{ int[ A_{x}·a^{2}·(q+(-W)) ]d[y] }·f(x,y)

G(x,y) = e^{ int[ A_{y}·a^{2}·(W+(-q)) ]d[x] }·g(x,y)

Ley:

d_{y}[F(x,y)]·d_{x}[G(x,y)] = 0 <==> ...

f(x,y) = e^{ int[ ia^{2}·A_{x}·(q+(-W)) ]d[y] }

g(x,y) = e^{ int[ ia^{2}·A_{y}·(W+(-q)) ]d[x] }

Ley:

Sea A(y,x) = (1/m)·< y,x > ==>

F(x,y)·G(x,y) = e^{ Potencial[ A(y,x)·a^{2}·< q+(-W),W+(-q) > ] }·f(x,y)·g(x,y)

d_{x}[F(x,y)]·d_{y}[G(x,y)] = ...

... d_{x}[f(x,y)]·d_{y}[g(x,y)]+( A_{y}·A_{x} )·a^{4}·(q+(-W))·(W+(-q))·f(x,y)·g(x,y)

Deducción:

F(x,y) = e^{ int[ A_{y}·a^{2}·(q+(-W)) ]d[x] }·f(x,y)

G(x,y) = e^{ int[ A_{x}·a^{2}·(W+(-q)) ]d[y] }·g(x,y)

Gravito-débil de leptones orbitales:

Ley:

F(t)·G(t) = e^{(1/m)·(p+(-Z))}·e^{(1/m)·(Z+(-p))}·f(t)·g(t)

d_{t}[F(t)]·d_{t}[G(t)] = ...

... d_{t}[f(t)]·d_{t}[g(t)]+(1/m)^{2}·d_{t}[p+(-Z)]·d_{t}[Z+(-p)]·f(t)·g(t)

Ley:

Sea A(x,y) = (1/m)·< x,y > ==>

F(x,y)·G(x,y) = e^{ Anti-Potencial[ A(x,y)·a^{2}·< p+(-Z),Z+(-p) > ] }·f(x,y)·g(x,y)

d_{y}[F(x,y)]·d_{x}[G(x,y)] = ...

... d_{y}[f(x,y)]·d_{x}[g(x,y)]+( A_{x}·A_{y} )·a^{4}·(p+(-Z))·(Z+(-p))·f(x,y)·g(x,y)

Ley:

Sea A(y,x) = (1/m)·< y,x > ==>

F(x,y)·G(x,y) = e^{ Potencial[ A(y,x)·a^{2}·< p+(-Z),Z+(-p) > ] }·f(x,y)·g(x,y)

d_{x}[F(x,y)]·d_{y}[G(x,y)] = ...

... d_{x}[f(x,y)]·d_{y}[g(x,y)]+( A_{y}·A_{x} )·a^{4}·(p+(-Z))·(Z+(-p))·f(x,y)·g(x,y)

Desintegración alfa:

Ley:

F(t)·G(t) = e^{(1/m)·(n·(q+(-q))+W+(-q))}·e^{(1/m)·(q+(-W))}·f(t)·g(t)

d_{t}[F(t)]·d_{t}[G(t)] = ...

... d_{t}[f(t)]·d_{t}[g(t)]+(1/m)^{2}·d_{t}[n·(q+(-q))+W+(-q)]·d_{t}[q+(-W)]·f(t)·g(t)

Ley:

Sea A(x,y) = (1/m)·< x,y > ==>

F(x,y)·G(x,y) = e^{ Anti-Potencial[ A(x,y)·a^{2}·< n·(q+(-q))+W+(-q),q+(-W) > ] }·f(x,y)·g(x,y)

d_{y}[F(x,y)]·d_{x}[G(x,y)] = ...

... d_{y}[f(x,y)]·d_{x}[g(x,y)]+( A_{x}·A_{y} )·a^{4}·(n·(q+(-q))+W+(-q))·(q+(-W))·f(x,y)·g(x,y)

Desintegración beta:

Ley:

F(t)·G(t) = e^{(1/m)·(n·(q+(-q))+q+(-W))}·e^{(1/m)·(W+(-q))}·f(t)·g(t)

d_{t}[F(t)]·d_{t}[G(t)] = ...

... d_{t}[f(t)]·d_{t}[g(t)]+(1/m)^{2}·d_{t}[n·(q+(-q))+q+(-W)]·d_{t}[W+(-q)]·f(t)·g(t)

Ley:

Sea A(x,y) = (1/m)·< x,y > ==>

F(x,y)·G(x,y) = e^{ Anti-Potencial[ A(x,y)·a^{2}·< n·(q+(-q))+q+(-W),W+(-q) > ] }·f(x,y)·g(x,y)

d_{y}[F(x,y)]·d_{x}[G(x,y)] = ...

... d_{y}[f(x,y)]·d_{x}[g(x,y)]+( A_{x}·A_{y} )·a^{4}·(n·(q+(-q))+q+(-W))·(W+(-q))·f(x,y)·g(x,y)

Desintegración gamma:

Ley:

F(t)·G(t) = e^{(1/m)·n·(q+(-q))}·e^{(1/m)·(W+(-W))}·f(t)·g(t)

d_{t}[F(t)]·d_{t}[G(t)] = ...

... d_{t}[f(t)]·d_{t}[g(t)]+(1/m)^{2}·d_{t}[n·(q+(-q))]·d_{t}[W+(-W)]·f(t)·g(t)

Ley:

Sea A(x,y) = (1/m)·< x,y > ==>

F(x,y)·G(x,y) = e^{ Anti-Potencial[ A(x,y)·a^{2}·< n·(q+(-q)),W+(-W) > ] }·f(x,y)·g(x,y)

d_{y}[F(x,y)]·d_{x}[G(x,y)] = ...

... d_{y}[f(x,y)]·d_{x}[g(x,y)]+( A_{x}·A_{y} )·a^{4}·n·(q+(-q))·(W+(-W))·f(x,y)·g(x,y)

Teorema:

x^{4}+ax^{2}+bx+c = 0 es resoluble

Demostración:

Sea x = u+iv ==>

(u+iv)^{4}+a·(u+iv)^{2}+b·(u+iv)+c = 0

(-6)·(uv)^{2}+2ai·(uv)+c = 0

uv = (1/(6i))·( (-a)+( a^{2}+(-1)·6c )^{(1/2)} ) ...

... || ...

uv = (1/(6i))·( (-a)+(-1)·( a^{2}+(-1)·6c )^{(1/2)} )

4i·(uv)·( u^{2}+(-1)·v^{2} ) = w·( u^{2}+(-1)·v^{2} )

w = (2/3)·( (-a)+( a^{2}+(-1)·6c )^{(1/2)} )

... || ...

w = (2/3)·( (-a)+(-1)·( a^{2}+(-1)·6c )^{(1/2)} )

u^{4}+(a+w)·u^{2}+bu = 0

v^{4}+(-1)·(a+w)·v^{2}+biv = 0

u^{3}+(a+w)·u+b = 0

v^{3}+(-1)·(a+w)·v+bi = 0

Teorema:

x^{5}+ax^{3}+bx^{2}+cx+d = 0 es resoluble

Demostración:

Sea x = u+iv ==>

(u+iv)^{5}+a·(u+iv)^{3}+b·(u+iv)^{2}+c·(u+iv)+d = 0

2bi·(uv) = d

uv = (d/(2bi))

El polinomio tiene 1 punto fijo,

y el coeficiente de Galois es n+2 = 3 y es resoluble

[Ah][ h es solución de uv ]

3a·(uv)·(u+iv)+10·(uv)^{2}·(u+iv) = w·(u+iv)

w = 3a·(d/(2bi))+10·(d/(2bi))^{2}

5·(uv)·(u^{3}+(-i)·v^{3}) = k·(u^{3}+(-i)·v^{3})

k = 5·(d/(2bi))

u^{5}+(a+k)·u^{3}+bu^{2}+(c+w)·u = 0

iv^{5}+(-i)·(a+k)·v^{3}+(-1)·bv^{2}+(ci+w)·v = 0

u^{4}+(a+k)·u^{2}+bu+(c+w) = 0

iv^{4}+(-i)·(a+k)·v^{2}+(-1)·bv+(ci+w) = 0

Teorema:

x^{6}+ax^{4}+bx^{3}+cx^{2}+dx+p = 0 es irresoluble

Demostración:

(-20)·i·(uv)^{3}+(-6)·a·(uv)^{2}+2ic·(uv)+p·(uv)^{0} = 0

F(uv) = vu = uv

El polinomio tiene 3 puntos fijos,

y el coeficiente de Galois es n+2 = 5 y es irresoluble

[Eh][ h no es solución de uv ]

uv = (z+(-1)·(1/10i)·a)

h^{3}+ph+q = 0

h | 1 | h | p+h^{2} | q+ph+h^{3} = 0

(z+(-h))·( z^{2}+hz+(p+h^{2}) ) = 0

uv = (1/10i)·a+( (1/2)·( (-h)+( h^{2}+(-4)·(h^{2}+p) )^{(1/2)} )

uv = (1/10i)·a+( (1/2)·( (-h)+(-1)·( h^{2}+(-4)·(h^{2}+p) )^{(1/2)} )

Teorema:

x^{7}+ax^{5}+bx^{4}+cx^{3}+dx^{2}+px+q = 0 es resoluble

Demostración:

(-6)·b·(uv)^{2}+2id·(uv)+q·(uv)^{0} = 0

F(uv) = vu = uv

El polinomio tiene 2 puntos fijos,

y el coeficiente de Galois es n+2 = 4 y es resoluble

[Ah][ h es solución de uv ]

Definición: [ de Grupo Galois ]

F(uv) = vu = uv

F(uv·ab) = F(uv)·ba 

F(ab·uv) = ba·F(uv)

Teorema:

F((uv·ab)·pq) = F(uv·(ab·pq))

Demostración:

F((uv·ab)·pq) = F(uv·ab)·qp = ( F(uv)·ba )·qp = (vu·ba)·qp = vu·(ba·qp) = ...

... vu·( ba·F(pq) ) = vu·F(ab·pq) = F(uv·(ab·pq))

Teorema:

F(uv·(uv)^{0}) = F(uv)

Demostración:

F(uv·(uv)^{0}) = F(uv)·(vu)^{0} = vu·(vu)^{0} = (vu)^{1+0} = vu = F(uv)

Teorema:

F(uv·(uv)^{(-1)}) = F( (uv)^{0} )

Demostración:

F(uv·(uv)^{(-1)}) = F(uv)·(vu)^{(-1)} = vu·(vu)^{(-1)} = (vu)^{1+(-1)} = (vu)^{0} = F( (uv)^{0} )

Teorema:

F(uv·ab) = F(ab·uv)

Demostración:

F(uv·ab) = F(uv)·ba = vu·ba = ba·vu = ba·F(uv) = F(ab·uv)

F(uv·ab) = vu·F(ab) = vu·ba = ba·vu = F(ab)·vu = F(ab·uv)

Definición: [ de coeficiente de Galois de un polinomio ]

Sea P(x) = P_{2n}(u+iv) ==>

Gal(P(x)) = Grado( Q_{n}(uv) )+2 = n+2

Sea P(x) = P_{2n+1}(u+iv) ==>

Gal(P(x)) = Grado( Q_{n+(-1)}(uv) )+2 = n+1

Teorema fundamental del Álgebra:

P_{n+1}(x) = P_{n}(x)·(x+(-1)·a_{n+1}) = (x+(-1)·a_{1})...(n)...(x+(-1)·a_{n})·(x+(-1)·a_{n+1})

Definición:

P(x) es resoluble <==> Grado[P(x)]+(-1)·Gal(P(x)) =[2]= Grado[P(x)]

P(x) es irresoluble <==> ¬( Grado[P(x)]+(-1)·Gal(P(x)) =[2]= Grado[P(x)] )

Teorema:

Sea P(x) = P_{2n}(u+iv) ==>

Si Gal(P(x)) = 2k+1 >] 5 ==> P(x) es irresoluble

Si Gal(P(x)) = 2k >] 5 ==> P(x) es resoluble

Demostración:

Por el teorema fundamental del Álgebra:

P_{2n}(u+iv) tiene 2n raíces

Por Cardano:

Q_{n}(uv) tiene n raíces

Sea Gal(P(x)) = n+2 = 2k+1 ==>

2n+(-1)·(2k+1) = 2·(n+(-k))+1 = 2p+1 =[2]= 1 & ¬( 1 =[2]= 2n )

P(x) es irresoluble

Sea Gal(P(x)) = n+2 = 2k ==>

2n+(-1)·2k = 2·(n+(-k)) = 2p =[2]= 0 & 0 =[2]= 2n

P(x) es resoluble

Teorema:

Sea P(x) = P_{2n+1}(u+iv) ==>

Si Gal(P(x)) = 2k+1 >] 5 ==> P(x) es irresoluble

Si Gal(P(x)) = 2k >] 5 ==> P(x) es resoluble

Demostración:

Por el teorema fundamental del Álgebra:

P_{2n+1}(u+iv) tiene 2n+1 raíces

Por Cardano:

Q_{n+(-1)}(uv) tiene n+(-1) raíces

Gal(P(x)) = n+1

Si n = 2k ==>

2n+1+(-1)·(2k+1) =[2]= 0  & ¬( 0 =[2]= 2n+1 )

P(x) es irresoluble

Si n = 2k+1 ==>

2n+1+(-1)·(2k+2) =[2]= (-1) =[2]= 1  & ( 1 =[2]= 2n+1 )

P(x) es resoluble

Teorema:

Sea f(x) continua ==>

Si [Ax][ x >] 0 ==> f(x) >] x ] ==> [Ec][ f(c) = 0 ]

Sea f(x) continua ==>

Si [Ax][ x [< 0 ==> f(x) [< x ] ==> [Ec][ f(c) = 0 ]

Demostración:

Sea u >] 0 ==>

f(u) >] u >] 0

(-1)·f(-u) [< (-u) [< 0

Teorema:

Sea a [< b ==>

Si f(x) = 2x+(-1)·(a+b) ==> [Ec][ f(c) = 0 ]

Sea a >] b ==> 

Si f(x) = 2x+(-1)·(a+b) ==> [Ec][ f(c) = 0 ]

Demostración:

f(b) = b+(-a) >] 0

f(a) = a+(-b) [< 0

Teorema:

Sea f(x) = x^{2n+1}+(-a) ==> [E!c][ f(c) = 0 ]

Demostración:

Se define c = a^{( 1/(2n+1) )}

d_{x}[f(x)] = (2n+1)·x^{2n} >] 0

f(x) es creciente

Sea s >] 0 ==>

f(c+s) = (c+s)^{2n+1}+(-a) >] c^{2n+1}+(-a) = 0

f(c+(-s)) = (c+(-s))^{2n+1}+(-a) [< c^{2n+1}+(-a) = 0

Teorema:

Sea f(x) = x^{2n+2}+(-x) ] ==> [E!c][ d_{x}[f(c)] = 0 ]

Demostración:

d_{x}[f(x)] = (2n+2)·x^{2n+1}+(-1)

Se define c = ( 1/(2n+2) )^{( 1/(2n+1) )}

d_{xx}^{2}[f(x)] = (2n+2)·(2n+1)·x^{2n} >] 0

d_{x}[f(x)] es creciente

Sea s >] 0 ==>

d_{x}[f(c+s)] = (2n+2)·(c+s)^{2n+1}+(-1) >] (2n+2)·c^{2n+1}+(-1) = 0

d_{x}[f(c+(-s))] = (2n+2)·(c+(-s))^{2n+1}+(-1) [< (2n+2)·c^{2n+1}+(-1) = 0

Problema:

Demostrad:

Sea f(x) = x^{[2n+1:b]}+(-a) ==> [E!c][ f(c) = 0 ]

Arte:

[Ef(x)][ Si ( F(x) = int[ f(x) ]d[x] & lim[x = 0][ F(x) ] = ( 1 || (-1) ) ) ==> ...

... int[x = (-2)]-[2][ f(x) ]d[x] = 0 ]

Exposición:

f(x) = 0·(1/x)

F(x) = x^{0}

int[x = (-2)]-[2][ f(x) ]d[x] = 2^{0}+(-1)·(-2)^{0} = 1+(-1) = 0

Destructor:

int[x = (-2)]-[2][ f(x) ]d[x] = F(2)+(-1)·F(-2) = F(1+1)+F((-1)+(-1)) = F(1+(-1))+(-1)·F((-1)+1) = ...

... F(0)+(-1)·F(0) = 0·F(0) = 0

Arte:

[Ef(x)][ Si ( F(x) = int[ f(x) ]d[x] & lim[x = 1][ F(x) ] = 2n ) ==> ...

... int[x = (1/(2n))]-[(1/n)][ f(2nx) ]d[x] = 0 ]

Exposición:

f(x) = 2n·0·(1/x)

F(x) = 2nx^{0}

int[x = (1/(2n))]-[(1/n)][ f(2nx) ]d[x] = (1/(2n))·( 2n2^{0}+(-1)·2n1^{0} ) = 0

Destructor:

int[x = (1/(2n))]-[(1/n)][ f(2nx) ]d[x] = (1/(2n))·( F(2)+(-1)·F(1) ) = ...

... (1/(2n))·( F( (3/2)+(1/2) )+(-1)·F(1) = (1/(2n))·( F( (3/2)+(-1)·(1/2) )+(-1)·F(1) ) = ...

... (1/(2n))·( F(1)+(-1)·F(1) ) = (1/(2n))·2n·0 = 0

Teorema:

Sea F(x) = int[ f(x) ]d[x] ==> 

Si lim[y = oo][ F(y) ] = c ==> lim[y = oo][ int[x = a]-[b][ f(x+y) ]d[x] ] = 0c

Demostración:

lim[y = oo][ int[x = a]-[b][ f(x+y) ]d[x] ] = lim[y = oo][ F(b+y)+(-1)·F(a+y) ] = ...

... F(b+oo)+(-1)·F(a+oo) = F(oo)+(-1)·F(oo) = 0c

Teorema:

lim[y = (1/k)][ int[x = (-1)]-[1][ (1/2)·(2n+1)·y·(xy)^{2n} ]d[x] ] ] = (1/k)^{2n+1}

Dual:

No estaba buena de cuerpo y cara ni tenía un cuerpo atlético.

Estaba buena de cuerpo y cara o tenía un cuerpo atlético.

Dual:

No estaba buena de cuerpo y cara y era fea.

Estaba buena de cuerpo y cara o era guapa.

Generador de destructor:

Estoy en un lugar haciendo esto,

no haciendo esto,

estoy haciendo esto.

Estoy en un lugar no haciendo esto,

haciendo esto,

no estoy haciendo esto.

Definición: [ de tensor de curvatura de Cristofel ]

d_{tt}^{2}[x_{s}]+R_{ijk}^{s}·d_{t}[x_{i}]·d_{t}[x_{j}]·d_{tt}^{2}[x_{k}] = 0

Teorema:

R_{kkk}^{k} = kt ==> x_{k}(t) = i·(1/k)^{(1/2)}·( t /o(t)o/ (1/2)·t^{2} )^{[o(t)o] (1/2)}

R_{ijk}^{s} = (ij)^{(1/2)}·t·(k/s)^{(1/2)}

Demostración:

(-1)·( 1/( d_{t}[x_{k}]^{2}·d_{tt}^{2}[x_{k}] ) )·d_{tt}^{2}[x_{k}] = R_{kkk}^{k} = kt

(-1)·( t /o(t)o/ ( x_{k} )^{[o(t)o] 2} ) = k·(1/2)·t^{2}

x_{k}(t) = i·(1/k)^{(1/2)}·( t /o(t)o/ (1/2)·t^{2} )^{[o(t)o] (1/2)}

Teorema:

R_{kkk}^{k} = e^{kt} ==> x_{k}(t) = ik·( t /o(t)o/ e^{kt} )^{[o(t)o] (1/2)}

R_{ijk}^{s} = e^{(1/2)·(i+j)·t}·(s/k)·e^{(1/2)·(k+(-s))·t}

Demostración:

(-1)·( 1/( d_{t}[x_{k}]^{2}·d_{tt}^{2}[x_{k}] ) )·d_{tt}^{2}[x_{k}] = R_{kkk}^{k} = kt

(-1)·( t /o(t)o/ ( x_{k} )^{[o(t)o] 2} ) = (1/k)·e^{kt}

x_{k}(t) = ik·( t /o(t)o/ e^{kt} )^{[o(t)o] (1/2)}

Homologías de Jûanagoras-Schoze:

Arte:

Sea h_{n}: S_{n} ---> S_{n+1} ==>

[En][Ef(x)][ f: S_{1} ---> S_{n} & f(x) es biyectiva ]

Exposición:

n = 1

Se define f(x) = x

h(n) = 1

Arte:

Sea h_{n}: S_{n} ---> S_{n+1} ==>

[En][Eg(x)][ g: S_{1} ---> S_{n+1} & g(x) es biyectiva ]

Exposición:

n = 0

Se define g(x) = x

h(n) = 0

Arte:

Sea h_{n}: P_{n}(A) ---> P_{n+1}(A) ==>

[En][Ef(x)][ f: A ---> P_{n}(A) & f(x) es biyectiva ]

Exposición:

n = 1

Se define f(x) = {x}

h(n) = 1

Arte:

Sea h_{n}: P_{n}(A) ---> P_{n+1}(A) ==>

[En][Eg(x)][ g: A ---> P_{n+1}(A) & g(x) es biyectiva ]

Exposición:

n = 0

Se define g(x) = {x}

h(n) = 0

Teorema:

Sea h_{n}: ( Z/[n]_{m} ) ---> ( Z/[n+1]_{m} ) ==>

[Ef(x)][ f: [0,m+(-1)]_{N} ---> ( Z/[n]_{m} ) & f(x) es biyectiva ]

Demostración:

Sea n = mk+r ==>

Se define f(r) = [r]_{m}

Teorema:

Sea h_{n}: ( Z/[n]_{m} ) ---> ( Z/[n+1]_{m} ) ==>

[Eg(x)][ g: [0,m+(-1)]_{N} ---> ( Z/[n+1]_{m} ) & g(x) es biyectiva ]

Demostración:

Sea n = mk+(r+(-1)) ==>

n+1 = mk+r

Se define g(r+(-1)) = [r]_{m}

Teorema:

Sea h_{n}: A x..(n)...x A ---> A x..(n+1)...x A ==>

[Ef(x)][ f: A ---> A x..(n)...x A & f(x) es biyectiva ]

Teorema:

Sea h_{n}: A x..(n)...x A ---> A x..(n+1)...x A ==>

[Eg(x)][ g: A ---> A x..(n+1)...x A & g(x) es biyectiva ]

Teorema:

Sea H(x) inyectiva ==>

Sea h_{n}: {n·( H(x) )} ---> {(n+1)·( H(x) )} ==>

[Ef(x)][ f: {x} ---> {n·( H(x) )} & f(x) es biyectiva ]

Teorema:

Sea H(x) inyectiva ==>

Sea h_{n}: {n·( H(x) )} ---> {(n+1)·( H(x) )} ==>

[Eg(x)][ g: {x} ---> {(n+1)·( H(x) )} & g(x) es biyectiva ]

Teorema:

Sea h_{n}: {nx} ---> {(n+1)·x} ==>

[Ef(x)][ f: {x} ---> {nx} & f(x) es biyectiva ]

Teorema:

Sea h_{n}: {nx} ---> {(n+1)·x} ==>

[Eg(x)][ g: {x} ---> {(n+1)·x} & g(x) es biyectiva ]

Teorema:

Sea H(x) inyectiva ==>

Sea h_{n}: {( H(x) )^{n}} ---> {( H(x) )^{n+1}} ==>

[Ef(x)][ f: {x} ---> {( H(x) )^{n}} & f(x) es biyectiva ]

Teorema:

Sea H(x) inyectiva ==>

Sea h_{n}: {( H(x) )^{n}} ---> {( H(x) )^{n+1}} ==>

[Eg(x)][ g: {x} ---> {( H(x) )^{n+1}} & g(x) es biyectiva ]

Teorema:

Sea h_{n}: {x^{n}} ---> {x^{n+1}} ==>

[Ef(x)][ f: {x} ---> {x^{n}} & f(x) es biyectiva ]

Teorema:

Sea h_{n}: {x^{n}} ---> {x^{n+1}} ==>

[Eg(x)][ g: {x} ---> {x^{n+1}} & g(x) es biyectiva ]

Definición:

F(x) es un morfismo topológico expansivo

<==>

[EG(x)][ x [<< G(x) & F(x) [<< F(G(x)) & ...

... F( A [&] B ) [<< F(G(A)) [&] F(G(B)) & ...

... F( A [ || ] B ) [<< F(G(A)) [ || ] F(G(B)) ]

F(x) es un morfismo topológico contractivo

<==>

[EG(x)][ x >>] G(x) & F(x) >>] F(G(x)) & ...

... F( A [&] B ) >>] F(G(A)) [&] F(G(B)) & ...

... F( A [ || ] B ) >>] F(G(A)) [ || ] F(G(B)) ]

Teorema:

Sea x [<< G(x) ==>

Si F(x) = x ==> F(x) es un morfismo topológico expansivo

Teorema:

Sea x >>] G(x) ==>

Si F(x) = x  ==> F(x) es un morfismo topológico contractivo

Teorema:

Sea x [<< G(x) ==>

Si F(x) = x [ || ] C ==> F(x) es un morfismo topológico expansivo

Demostración:

F(x) = x [ || ] C [<< G(x) [ || ] C = F(G(x))

F( A [&] B ) = ( A [&] B ) [ || ] C = ( A [ || ] C ) [&] ( B [ || ] C ) [<< ...

... ( G(A) [ || ] C ) [&] ( G(B) [ || ] C ) = F(G(A)) [&] F(G(B))

F( A [ || ] B ) = ( A [ || ] B ) [ || ] C = ( A [ || ] B ) [ || ] ( C [ || ] C ) = ( A [ || ] C ) [ || ] ( B [ || ] C ) [<< ...

... ( G(A) [ || ] C ) [ || ] ( G(B) [ || ] C ) = F(G(A)) [ || ] F(G(B))

Teorema:

Sea x >>] G(x) ==>

Si F(x) = x [&] C ==> F(x) es un morfismo topológico contractivo

Definición:

{x} , {y} = { z : ( z = x || z = y ) } = {x,y}

}x{ ; }y{ = { z : ( z != x & z != y ) } = }x;y{

Teorema:

{x} , {x} = { z : ( z = x || z = x ) } = { z : z = x } = {x}

}x{ ; }x{ = { z : ( z != x & z != x ) } = { z : z != x } = }x{

Teorema:

{x} , 0 = { z : ( z = x || z != z ) } = { z : z = x } = {x}

}x{ ; 1 = { z : ( z != x & z = z ) } = { z : z != x } = }x{

Teorema:

Sea G(x) = x,z_{1},...,z_{n} ==>

Si F(x) = {x} ==> F(x) es un morfismo topológico expansivo

Demostración:

F(x) = {x} [<< {G(x)} = F(G(x))

F(x , y) = {x , y} = {x} , {y} [<< {G(x)} , {G(y)} = F(G(x)) , F(G(y))

Teorema:

Sea G(x) = x;z_{1};...;z_{n} ==>

Si F(x) = }x{  ==> F(x) es un morfismo topológico contractivo

Demostración:

F(x) = }x{ >>] }G(x){ = F(G(x))

F(x ; y) = }x ; y{ = }x{ ; }y{ >>] }G(x){ ; }G(y){ = F(G(x)) ; F(G(y))

Conjetura de Poincaré:

Teorema:

[EF][ Si ( y_{1}(ix) = e^{zix} & F( y_{1}(ix),z ) ) ==> ( lim[n = oo][ F( y_{n}(ix),z ) ] & z = 0 ) ]

Demostración:

Se define F( y_{n}(ix),z ) <==> ( y_{n}(ix) = e^{(1/n)·zix} & d_{ix}[ y_{n}(ix) ] = z·y_{n}(ix) )

d_{ix}[ 1^{zix} ] = d_{ix}[ 1^{ix} ] = 1^{ix}·ln(1) = 0

Teorema:

[EF][ Si ( y_{1}(ix) = re^{(z/r)·ix} & F( y_{1}(ix),z ) ) ==> ( lim[n = oo][ F( y_{n}(ix),z ) ] & z = r ) ]

Demostración:

Se define F( y_{n}(ix),z ) <==> ...

... ( y_{n}(ix) = re^{(1/n)·(z/r)·ix} & d_{ix}[ y_{n}(ix) ] = (1/(nr))·z·y_{n}(ix) )

d_{ix}[ 1^{(z/r)·ix} ] = d_{ix}[ 1^{ix} ] = 1^{ix}·ln(1) = 0

métodos-numéricos y topología-algebraica y óptica y arte-matemático y topología y números-figurados y medicina y dualogía

Teorema:

Sea d_{x}[y(x)] = y+x+(k+(-1)) ==>

[Ej][ (1/h)·( y_{n+1}+(-1)·y_{n} ) = y_{n}+j ] es un método numérico convergente a y(x)

Demostración:

Sea h = 0a & j = (-1)·((k/a)+1) ==>

y_{n+1} = y_{n}+h·( y_{n}+j ) = y_{n}·(1+h)+hj

y_{n+1} = y_{0}·(1+h)^{n}+nhj

Sea y_{0} = 1 ==>

y(a) = y_{oo} = e^{a}+(-k)+(-a)

Teorema:

Sea d_{x}[y(x)] = y+x^{2}+(k+(-2)) ==>

[Ej][ (1/h)·( y_{n+1}+(-1)·y_{n} ) = y_{n}+j ] es un método numérico convergente a y(x)

Demostración:

Sea h = 0a & j = (-1)·((k/a)+2+a) ==>

y_{n+1} = y_{n}+h·( y_{n}+j ) = y_{n}·(1+h)+hj

y_{n+1} = y_{0}·(1+h)^{n}+nhj

Sea y_{0} = 1 ==>

y(a) = y_{oo} = e^{a}+(-k)+(-1)·2a+(-1)·a^{2}

Teorema: [ de sp-line cuadrática ]

P(x) = (x+(-1)·x_{j})·(x+(-1)·x_{k})·( (x_{i}+(-1)·x_{j})·(x_{i}+(-1)·x_{k}) )^{(-1)}·f(x_{i})

Teorema: [ de sp-line cúbica ]

Q(x) = ...

... (x+(-1)·x_{j})·x·(x+(-1)·x_{k})·( (x_{i}+(-1)·x_{j})·x_{i}·(x_{i}+(-1)·x_{k}) )^{(-1)}·f(x_{i})

Teorema:

Sea ( m != 1 & d_{x}[y(x)] = y^{m} ) ==>

[Ej][ (1/h)·( y_{n+1}+(-1)·( y_{n} )^{j} ) = ( y_{n} )^{m} ] es un método numérico convergente a y(x)

Demostración:

Sea h = 0 & j = ( 1/(1+(-m))^{0} ) ==>

y_{n+1} = ( y_{n} )^{j}+h·( y_{n} )^{m} = ( y_{n} )^{m+[j+(-m):h]}

y_{n+1} = ( y_{1} )^{( 1/(1+(-m)) )^{0n}}

Sea y_{1} = (1+(-m))·a ==>

y(a) = y_{oo} = ( (1+(-m))·a )^{( 1/(1+(-m)) )}

Teorema:

Sea m != 1 ==>

Si  a_{n+1} = (1/2)·( a_{n}+( a_{n} )^{m}·y_{n} ) ==> a_{oo} = ( y_{n} )^{( 1/(1+(-m)) )}

Demostración:

( a_{oo} )^{1+(-m)} = (1/2)·( ( a_{oo} )^{1+(-m)}+y_{n} )

2·( a_{oo} )^{1+(-m)}+(-1)·( a_{oo} )^{1+(-m)} = y_{n}

( a_{oo} )^{1+(-m)} = y_{n}

a_{oo} = ( y_{n} )^{( 1/(1+(-m)) )}

Teorema:

Sea f_{n}(x): ( x+(-a) )^{n} ---> ( x+(-a) )^{n+1} ==>

[Ex][ f_{n}(x) está compactificada en 2 clases ]

Teorema:

Sea f_{n}(x): ( e^{x}+(-a) )^{n} ---> ( e^{x}+(-a) )^{n+1} ==>

[Ex][ f_{n}(x) está compactificada en 2 clases ]

Teorema:

Sea f_{n}(P(x)): d_{x...x}^{n}[P(x)]·h(x) ---> Q(x) [o(x)o] ( x /o(x)o/ H(x) ) ==>

[EP(x)][ f_{n}(P(x)) está compactificada en 2 clases ]

Demostración:

d_{x}[ sinh(x) [o(x)o] ( x /o(x)o/ H(x) ) ]·h(x) = cosh(x)

d_{x}[ cosh(x) [o(x)o] ( x /o(x)o/ H(x) ) ]·h(x) = sinh(x)

Ley:

d_{z}[f(z(t),x,t)]+d_{x}[f(z(t),x,t)] = (1/S)·vt+a·(1/(ax))^{n}

f(z(t),x,t) = (1/S)·(1/2)·vt^{2} [o(t)o] z(t)+( (ax) /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

Ley:

d_{z}[f(z(t),x,t)]+d_{x}[f(z(t),x,t)] = (1/S)·(1/2)·(q/m)·gt^{2}+a·(1/(ax))^{n}

f(z(t),x,t) = (1/S)·(1/6)·(q/m)·gt^{3} [o(t)o] z(t)+( (ax) /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

Problema:

d_{z}[f(z(t),x,t)]+d_{x}[f(z(t),x,t)] = (1/S)·(1/6)·(I/m)·gt^{3}+a·(1/(ax))^{n}

Ley:

Sea d[...(n)...d[q]...(n)...] = n!·qa^{n}·d[z]...(n)...d[z] ==>

F(z) = pq(z)·k·(1/r)^{3}·z 

z(t) = ( n·( (1/(4+2n))·(1/m)·pqk·(1/r)^{3}·a^{n} )^{(1/2)}·t )^{(-1)·(2/n)}

d_{t}[q(t)] = n!·qa^{n}·(-2)·n^{(-2)}·( (1/(4+2n))·(1/m)·pqk·(1/r)^{3}·a^{n} )^{(-1)}·t^{(-3)}

Artes de Vinogradov energéticos:

Arte:

Sea 0 [< p [< 2 ==>

[En][ 2^{(2p+1)·sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+2^{2p+1}+(2p+1) ]

Arte:

[En][ 2^{sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+3 ]

[En][ 8^{sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+11 ]

[En][ 32^{sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+37 ]

Arte:

Sea 1 [< p [< 2 ==>

[En][ 2^{(2p)·sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+2^{2p}+(2p+(-1)) ]

Arte:

[En][ 4^{sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+5 ]

[En][ 16^{sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+19 ]

Arte:

Sea 1 [< p [< 3 ==>

[En][ 3^{p·sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+3^{p}+4 ]

Arte:

[En][ 3^{sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+7 ]

[En][ 9^{sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+13 ]

[En][ 27^{sum[k = 1][n][k]} < ln( sum[k = 1][n][k] )+31 ]

Arte:

Sea 1 [< p [< 3 ==>

[En][ (5+6p)·sum[k = 1][n][k] < ln( sum[k = 1][n][k] )+( 5+(6p+6) ) ]

Arte:

[En][ 11·sum[k = 1][n][k] < ln( sum[k = 1][n][k] )+17 ]

[En][ 17·sum[k = 1][n][k] < ln( sum[k = 1][n][k] )+23 ]

[En][ 23·sum[k = 1][n][k] < ln( sum[k = 1][n][k] )+29 ]

Teorema:

Sea ( h(1) = 1 & h(1/n) creciente ) ==>

Si E_{n,s} = { x : 0 [< m(x,y) [< h(1/n)·s } ==> ...

... Si ( E_{n,s} [<< B & E_{m,d} [<< B ) ==> E_{n,s} [ || ] E_{m,d} [<< B

... Si ( E_{n,s} [<< B & E_{m,d} [<< B ) ==> E_{n,s} [&] E_{m,d} [<< B

... E_{n} puede estar compactificada en m clases.

Demostración:

A_{1} = E_{1} = { x : 0 [< m(x,y) [< s }

A_{n+1} = E_{n} [ \ ] E_{n+1} = { x : h( 1/(n+1) )·s < m(x,y) [< h(1/n)·s }

Teorema:

Sea ( h(0) = 0 & h(n) creciente ) ==>

Si E_{n} = { x : 0 [< x [< h(n) } ==> ...

... Si ( E_{n} [<< B & E_{m} [<< B ) ==> E_{n} [ || ] E_{m} [<< B

... Si ( E_{n} [<< B & E_{m} [<< B ) ==> E_{n} [&] E_{m} [<< B

... E_{n} puede estar compactificada en m clases.

Demostración:

A_{0} = E_{0} = {0}

A_{n+1} = E_{n+1} [ \ ] E_{n} = { x :  h(n) < x [< h(n+1) }

Teorema:

Sea n >] 1 ==>

sum[k = 1]-[n][ (2k+(-1)) ] = n^{2}

Demostración: [ por geometría ]

a_{1}:

1

a_{2}:

010

111

a_{3}:

00100

01110

11111

a_{n} = (2n+(-1))·n+(-1)·n·(n+(-1)) = (2n^{2}+(-n))+(-1)·(n^{2}+(-n)) = n^{2}

Teorema:

Sea n >] 1 ==>

sum[k = 1]-[n][ (2k+(-1)) ]+(2n+(-1))^{2} = 5n^{2}+(-1)·4n+1

Demostración: [ por geometría ]

a_{1}:

1

1

a_{2}:

010

111

111

111

111

a_{n} = n^{2}+(2n+(-1))^{2} = n^{2}+(4n^{2}+(-1)·4n+1) = 5n^{2}+(-1)·4n+1

Teorema: [ de números cuadrados perimetrales ]

Sea n >] 1 ==>

(2n+(-1))^{2}+(-1)·(2n+(-3))^{2} = 8n+(-8)

Demostración: [ por geometría ]

a_{1}:

0

a_{2}:

111

101

111

a_{3}:

11111

10001

10001

10001

11111

a_{n} = (2n+(-1))^{2}+(-1)·(2n+(-3))^{2} = (4n^{2}+(-1)·4n+1)+(-1)·(4n^{2}+(-1)·12n+9) = 8n+(-8)

Principio: [ de pitagorancias orgánicas ]

n = 1

Sal = Na-Cl

n = 2

Azúcar = A-O-A

n = 3

Hierro = A-Fe=Fe-A

n = 4

Iodo = A-IH=I=IH-A

Principio: [ de aparato de presión ]

Sea ( mv(t) la impulsión sanguínea & F(t) la fuerza del aparato de presión ) ==>

mv(t)·d_{t}[q] = q(t)·F(t)·(ut)^{n}

q(t) = qe^{( int[ F(t) ]d[t] /o(t)o/ int[ mv(t) ]d[t] ) [o(t)o] (1/u)·(1/(n+1))·(ut)^{n+1}}

Ley:

mv(t)·d_{t}[q] = q(t)·(Igt)·(ut)^{n}

q(t) = qe^{( (1/2)·Igt^{2} /o(t)o/ int[ mv(t) ]d[t] ) [o(t)o] (1/u)·(1/(n+1))·(ut)^{n+1}}

Ley:

mv(t)·d_{t}[q] = q(t)·(-b)·(r/t)·(ut)^{n}

q(t) = qe^{( (-b)·r·ln(ut) /o(t)o/ int[ mv(t) ]d[t] ) [o(t)o] (1/u)·(1/(n+1))·(ut)^{n+1}}

Principio: [ de analítica sanguínea ]

Sea ( mv(t) la impulsión sanguínea & F(t) la fuerza de centrifugación ) ==>

mv(t)·d_{t}[q] = qF(t)·(ut)^{n}

q(t) = q·( int[ F(t) ]d[t] /o(t)o/ int[ mv(t) ]d[t] ) [o(t)o] (1/u)·(1/(n+1))·(ut)^{n+1}

Ley:

mv(t)·d_{t}[q] = (1/(mr))·(qgt)^{2}·(ut)^{n}

q(t) = ( ( (1/(mr))·(1/3)·(qg)^{2}·t^{3} /o(t)o/ int[ mv(t) ]d[t] ) [o(t)o] (1/u)·(1/(n+1))·(ut)^{n+1} )

Ley:

mv(t)·d_{t}[q] = (1/(mr))·( (1/2)·Igt^{2} )^{2}·(ut)^{n}

q(t) = ( ( (1/(mr))·(1/20)·(Ig)^{2}·t^{5} /o(t)o/ int[ mv(t) ]d[t] ) [o(t)o] (1/u)·(1/(n+1))·(ut)^{n+1} )

Principio: [ de orina de humano ]

b(x,y,t) = int-int[ d_{xy}^{2}[ m(x,y) ] ]d[x]d[y]·u·f(ut)

M(x,y,t) = int[ b(x,y,t) ]d[t]

Ley: [ de sanidad de pitagorancia cero ]

Sea ( f(ut) = (ut)^{0} & d_{xy}^{2}[ m(x,y) ] = ma^{2} ) ==>

M(x,y,t) = mxya^{2}·(ut)

M(x,y,t) = mxya^{2} <==> t = (1/u)

Ley: [ de pitagorancia de materia sanguínea ]

Sea ( f(ut) = (ut)^{n} & d_{xy}^{2}[ m(x,y) ] = ma^{2} ) ==>

M(x,y,t) = mxya^{2}·(1/(n+1))·(ut)^{n+1}

M(x,y,t) = mxya^{2} <==> t = (1/u)·(n+1)^{( 1/(n+1)) }

Ley: [ de virus genético TACCCCAT-TCAAAACT ]

Sea ( f(ut) = (1/(ut)) & d_{xy}^{2}[ m(x,y) ] = ma^{2} ) ==>

M(x,y,t) = mxya^{2}·ln(ut)

M(x,y,t) = mxya^{2} <==> t = (1/u)·e

Principio: [ de heces de animal ]

k(x,y,t) = int-int[ d_{xy}^{2}[ m(x,y) ] ]d[x]d[y]·u^{2}·g(ut)

M(x,y,t) = int-int[ k(x,y,t) ]d[t]d[t]

Ley: [ de sanidad de pitagorancia cero ]

Sea ( g(ut) = 0·(1/(ut)) & d_{xy}^{2}[ m(x,y) ] = ma^{2} ) ==>

M(x,y,t) = mxya^{2}·(ut)

M(x,y,t) = mxya^{2} <==> t = (1/u)

Ley: [ de pitagorancia de materia sanguínea ]

Sea ( g(ut) = n·(ut)^{n+(-1)} & d_{xy}^{2}[ m(x,y) ] = ma^{2} ) ==>

M(x,y,t) = mxya^{2}·(1/(n+1))·(ut)^{n+1}

M(x,y,t) = mxya^{2} <==> t = (1/u)·(n+1)^{( 1/(n+1)) }

Ley: [ de virus genético TACCCCAT-TCAAAACT ]

Sea ( g(ut) = (-1)·(1/(ut))^{2} & d_{xy}^{2}[ m(x,y) ] = ma^{2} ) ==>

M(x,y,t) = mxya^{2}·ln(ut)

M(x,y,t) = mxya^{2} <==> t = (1/u)·e

Teorema:

int[ lim[n = oo][ ( 1/(1+nx) ) ] ]d[x] = int[ (1/oo)·( oo/(1+oox) ) ]d[x] = (1/oo)·ln(oo) = ln(2)

lim[n = oo][ int[ ( 1/(1+nx) ) ] ]d[x] = lim[n = oo][ (1/n)·ln(1+nx) ] = (1/oo)·ln(oo) = ln(2)

Ley:

Los hombres tenemos que rezar al Mal,

que los azeris vos caguéis encima,

pero que lleguéis al váter,

a cagar en la taza,

porque el Mal va a cambiar el rezo de cagar,

y lo vamos a destruir.

Los azeris tenéis que rezar al Mal,

que los hombres nos pijemos encima,

pero que lleguemos al váter,

a pijar en al taza,

porque el Mal va a cambiar el rezo de pijar,

y los vais a destruir.

Ley: [ de esquizofrenia ]

Hay condenación o no he fracasado en destruir a un dios del Mal.

Deducción:

La voz en la mente dice no hay condenación y has fracasado.

Principio: [ de drogas de polímeros de pitagorancia exponencial ]

I_{q}(x,y,t) = int-int-int[ ( q(t) )^{n} ]d[x]d[y]d[q]

Principio: [ de drogas de polímeros de pitagorancia de producto ]

I_{q}(x,y,t) = int-int-int-int[ n·( q(t) )^{n+(-1)} ]d[x]d[y]d[q]d[q]

Ley:

Sea q(t) = qe^{mut} ==>

I_{q}(x,y,t) = (1/(n+1))·q^{n+1}·e^{(n+1)·mut}·xy

Deducción:

I_{q}(x,y,t) = ...

... int[ int[ int-int[ nq^{n+(-1)}e^{(n+(-1))·mut} ]d[x]d[y]·qe^{mut}·mu ]d[t]·qe^{mut}·mu ]d[t]

Ley:

Sea z(t) = q·(ut)^{m} ==>

V(x,y,t) = (1/(n+1))·q^{n+1}·(ut)^{(n+1)·m}·xy

Ley:

Sea z(t) = q·(ut)^{m}+p ==>

V(x,y,t) = (1/(n+1))·q^{n+1}·(ut)^{(n+1)·[m:(p/q)]}·xy

Arte:

[En][ frac[k = 1]-[n][ ( (2k+(-1))/(1+(2k+1)) ) ] = (1/4)·n ]

Exposición:

n = 1

f(k) = 1

frac[k = 1]-[n][ ( (2f(k)+(-1))/(1+(2f(k)+1)) ) ] = frac[k = 1]-[n][ ( 1/(1+3) ) ] = ...

... frac[k = 1]-[n][ ( 1/(1+( 3+(1/2)+(-1)·(1/2) )) ) ] = frac[k = 1]-[n][ ( 1/(1+( 3+(1/2)+(1/2) )) ) ] = ...

... frac[k = 1]-[n][ ( 1/(1+(3+1)) ) ] = frac[k = 1]-[n][ ( 1/(1+4) ) ] = ...

... frac[k = 1]-[n+(-1)][ ( 1/(1+4) ) ] o 1+4 = frac[k = 1]-[n+(-1)][ ( 1/(1+4) ) ] o 1+(1/4) = ...

... (1/4)·(n+(-1))+(1/4) = (1/4)·n

Arte:

[En][ frac[k = 0]-[n][ ( k!/(1+(k+1)!) ) ] = (1/2)·(n+1) ]

Exposición:

n = 0

f(k) = 1

frac[k = 0]-[n][ ( f(k)!/(1+(f(k)+1)!) ) ] = frac[k = 0]-[n][ ( 1/(1+(1+1)!) ) ] = ...

... frac[k = 0]-[n][ ( 1/(1+2) ) ] = frac[k = 0]-[n+(-1)][ ( 1/(1+2) ) ] o 1+2 = ...

... frac[k = 0]-[n+(-1)][ ( 1/(1+2) ) ] o 1+(1/2) = (1/2)·n+(1/2) = (1/2)·(n+1)

Arte: [ de Rogers-Ramanujan ]

[En][ frac[k = 1]-[n][ ( q^{k}/(1+(-1)·q^{k+1}) ) ] = q·( 1/(1+(-1)·q^{2}) ) ]

Exposición:

n = 1

f(1) = (1/m)

g(1/m) = 0

frac[k = 1]-[n][ ( q^{k}/(1+(-1)^{f(1)}·q^{k+1}) ) ] = ...

... frac[k = 1]-[n][ ( q^{k}/(1+(-1)^{(1/m)}·q^{k+1}) ) ] = ...

... frac[k = 1]-[n][ ( q^{k}/(1+(-1)^{g(1/m)}·q^{k+1}) ) ] = ...

... frac[k = 1]-[n][ ( q^{k}/(1+q^{k+1}) ) ] = ...

... frac[k = 1]-[n+(-1)][ ( q^{k}/(1+q^{k+1}) ) ] o q^{n}+q^{2n+1} = ...

... q+...(n)...+q^{2n+(-1)}+q^{2n+1}

Arte: [ de Rogers-Ramanujan-Garriga ]

[En][ frac[k = 1]-[n][ ( q^{(1/k)}/(1+(-1)·q^{( 1/(k+1) )}) ) ] = q·( 1/(1+(-1)·q^{(1/2)}) ) ]

Exposición:

n = 1

f(1) = (1/m)

g(1/m) = 0

frac[k = 1]-[n][ ( q^{(1/k)}/(1+(-1)^{f(1)}·q^{( 1/(k+1) )}) ) ] = ...

... frac[k = 1]-[n][ ( q^{(1/k)}/(1+(-1)^{(1/m)}·q^{( 1/(k+1) )}) ) ] = ...

... frac[k = 1]-[n][ ( q^{(1/k)}/(1+(-1)^{g(1/m)}·q^{( 1/(k+1) )}) ) ] = ...

... frac[k = 1]-[n][ ( q^{(1/k)}/(1+q^{( 1/(k+1) )}) ) ] = ...

... frac[k = 1]-[n+(-1)][ ( q^{(1/k)}/(1+q^{( 1/(k+1) )}) ) ] o q^{(1/n)}+q^{(1/n)+(1/(n+1))} = ...

... q+sum[k = 1]-[n][ q^{(1/k)+(1/(k+1))} ] = ...

... q+sum[k = 1]-[n][ q^{( 1/(k·(k+1)) )·(2k+1)} ] = ...

... q+sum[k = 1]-[n][ q^{( k/(k+1) )·(2k+1)} ] = ...

... q+sum[k = 1]-[n][ q^{( k/(k+(1/2)+(1/2)) )·(2k+1)} ] = ...

... q+sum[k = 1]-[n][ q^{( k/(k+(1/2)+(-1)·(1/2)) )·(2k+1)} ] = ...

... q+sum[k = 1]-[n][ q^{2k+1} ] = q+sum[k = 1]-[n][ q^{(1/2)·k+1} ]

Dual:

La Luá está de-puá me avec sa-pá de-le-munt,

de-le-dans la cupuá de la Luá de La-Franç.

La Luá está-de-puá me avec sa-pá de-la-vall,

de-le-dans la ne cupuá de la Luá de La-Franç.

Morfosintaxis:

[A$1$ [z] ][ [z] és-de-puá Luá ]-[ [z] está de-puá P([a]) , Q([p]) ]

P([a]) <==> [ me avec sa-pá [a] ]-[ [a] és-de-puá de-le-munt ]

Q([p]) <==> [ de-le-dans [p(s)] ]-[A$1$ [p(s)] ][ [p(s)] és-de-puá cupuá de [s(w)] ]-...

... [A$1$ [s(w)] ][ [s(w)] és-de-puá Luá de [w] ]-[ [w] és-de-puá La-Franç ]

[A$1$ [z] ][ [z] és-de-puá Luá ]-[ [z] está de-puá P([b]) , Q([q]) ]

P([b]) <==> [ me avec sa-pá [b] ]-[ [b] és-de-puá de-la-vall ]

Q([q]) <==> [ de-le-dans [q(s)] ]-[A$1$ [q(s)] ][ [q(s)] és-de-puá ne cupuá de [s(w)] ]-...

... [A$1$ [s(w)] ][ [s(w)] és-de-puá Luá de [w] ]-[ [w] és-de-puá La-Franç ]

Definición: [ de dualogía ]

[Ey][ x@y & y@z ] <==> x = z

Teorema:

Si [Ec][ x+y = f(c) = z+y & f(c) = 0 ] ==> x+y = f(x) es dualogía

Definición:

Dual[ x+y = f(x) ] = { < x,y > : x+y = f(x) & f(x) = 0 }

Definición:

Gen[ x+y = f(x) ] = { < x,(-x) > = sum[k = 1]-[n][ a_{k}·< c_{k},(-1)·c_{k} > ] : ...

... < c_{k},(-1)·c_{k} > € Dual[ x+y = f(x) ] }

Teorema:

(1/2)·x^{2}+int[ y ]d[x] = F(x) es dualogía

Demostración:

x+y = f(x)

x·d[x]+y·d[x] = (x+y)·d[x] = f(x)·d[x]

int[ x ]d[x]+int[ y ]d[x] = int[ f(x) ]d[x]

(1/2)·x^{2}+int[ y ]d[x] = F(x)

Teorema:

Dual[ (1/2)·x^{2}+int[ y ]d[x] = x+(-a) ] = { < a,(-a) > }

< x,(-x) > = (x/a)·< a,(-a) >

< (-x),x > = (-1)·(x/a)·< a,(-a) >

Dual[ x+y = 1 ] = { < (1/n),1+(-1)·(1/n) > }

< p(z),¬p(z) > = < 0,0 >+< (1/n),1+(-1)·(1/n) >

< ¬q(z),q(z) > = < 1,1 >+(-1)·< (1/n),1+(-1)·(1/n) >

Demostración:

y = d_{x}[ int[ y ]d[x] ] = d_{x}[ (-1)·(1/2)·x^{2} ] = d_{a}[ (-1)·(1/2)·a^{2} ] = (-a)

Teorema:

Dual[ (1/2)·x^{2}+int[ y ]d[x] = (1/2)·x^{2}+(-1)·a^{2} ] = ...

... { 2^{(1/2)}·< a,(-a) > , 2^{(1/2)}·< (-a),a > }

Dual[ x+y = x ] = { < 1,0 > }

Teorema:

Dual[ (1/2)·x^{2}+int[ y ]d[x] = e^{x}+(-a) ] = { < ln(a),(-1)·ln(a) > }

Dual[ x+y = e^{x} ] = { < ln(0),ln(oo) > }

Teorema:

Si [Ec][ x·y = f(c) = z·y & f(c) = 1 ] ==> x·y = f(x) es dualogía

Definición:

Dual[ x·y = f(x) ] = { < x,y > : x·y = f(x) & f(x) = 1 }

Definición:

Gen[ x·y = f(x) ] = { < x,(1/x) > = sum[k = 1]-[n][ < a_{k},b_{k} >·< c_{k},( 1/(c_{k}) ) > ] : ...

... < c_{k},( 1/(c_{k}) ) > € Dual[ x·y = f(x) ]}

Teorema:

Si [Ec(t)][ x(t) [o(t)o] y(t) = f(c(t)) = z(t) [o(t)o] y(t) & f(c(t)) = t ] ==> ...

... x(t) [o(t)o] y(t) = f(x(t)) es dualogía

Definición:

Dual[ x(t) [o(t)o] y(t) = f(x(t)) ] = { < x(t),y(t) > : x(t) [o(t)o] y(t) = f(x(t)) & f(x(t)) = t }

Definición:

Gen[ x(t) [o(t)o] y(t) = f(x(t)) ] = { < x(t),( t /o(t)o/ x(t) ) > = ...

... sum[k = 1]-[n][ < a_{k}(t),b_{k}(t) > [o(t)o] < c_{k}(t),( t o(t)o/ c_{k}(t) ) > ] : ...

... < c_{k}(t),( t /o(t)o/ c_{k}(t) ) > € Dual[ x(t) [o(t)o] y(t) = f(x(t)) ]}

Teorema:

Si [Ec][ m(x,y) = f(c) = m(z,y) & f(c) = k ] ==> m(x,y) = f(x) es dualogía

Demostración:

m(x,y) = f(c) = m(z,y)

< x,y > = < z,y >

x = z

Se define < x,y > = < c,0 > = < z,y > & f(c) = m(c,0)

Definición:

Dual[ m(x,y) = f(x) ] = { < x,y > : m(x,y) = f(x) & f(x) = k }

Definición:

m(x,y) = | x+(-y) |

Teorema:

m(x,x) = 0

Demostración:

| x+(-x) | = 0

Teorema:

m(x,y) [< m(x,z)+m(z,y)

Demostración:

m(x,y) = | x+(-y) | = | x+(-z)+z+(-y) | [< | x+(-z) |+| z+(-y) | = m(x,z)+m(z,y)

Teorema:

Sea m(x,y) = | x+(-y) | = k ==>

Dual[ m(x,y) = f(x) ] = { < (n+1)·k,nk >,< nk,(n+1)·k > }

Teorema:

Sea m(x,y) = | x+(-y) | = |x|+(-a) ==>

Dual[ m(x,y) = f(x) ] = { < k+a,a >,< (-k)+(-a),(-a) > }

Teorema:

Sea m(x,y) = | x+(-y) | = x^{2}+(-a) ==>

Dual[ m(x,y) = f(x) ] = ...

... { < k^{(1/2)·[1:a]},k+k^{(1/2)·[1:a]} >,< k^{(1/2)·[1:a]},(-k)+k^{(1/2)·[1:a]} >,...

... < (-1)·k^{(1/2)·[1:a]},k+(-1)·k^{(1/2)·[1:a]} >,< (-1)·k^{(1/2)·[1:a]},(-k)+(-1)·k^{(1/2)·[1:a]} > }

Teorema:

|| < a,b >+< u,v > || [< || < a,b > ||+|| < u,v > ||

Demostración:

f(2·|a||b|) = 0

g(2·|u||v|) = 0

... || < a,b >+< u,v > || = ...

... ( (|a|+|u|)^{2}+(|b|+|v|)^{2} )^{(1/2)} [< |a|+|u|+|b|+|v| = |a|+|b|+|u|+|v| = ...

... ( |a|^{2}+2·|a||b|+|b|^{2} )^{(1/2)}+( |u|^{2}+2·|u||v|+|v|^{2} )^{(1/2)} [< ...

... ( |a|^{2}+f(2·|a||b|)+|b|^{2} )^{(1/2)}+( |u|^{2}+g(2·|u||v|)+|v|^{2} )^{(1/2)} =

... ( |a|^{2}+|b|^{2} )^{(1/2)}+( |u|^{2}+|v|^{2} )^{(1/2)} = || < a,b > ||+|| < u,v > || 

Definición:

m(x,y) = || x+yi ||

Teorema:

m(x,x) = 0

Demostración:

( (|a|+|ai|)^{2}+(|b|+|bi|)^{2} )^{(1/2)} = 0

Teorema:

m(x,y) [< m(x,z)+m(z,y)

Demostración:

( (|a|+|ui|)^{2}+(|b|+|vi|)^{2} )^{(1/2)} = ( (|a|+|mi|+|m|+|ui|)^{2}+(|b|+|ni|+|n|+|vi|)^{2} )^{(1/2)}

m(x,y) = || x+yi || = || x+zi+z+yi || [< || x+zi ||+|| z+yi || = m(x,z)+m(z,y)

Teorema:

Sea m(r,0) = ( |x|^{2}+|y|^{2} )^{(1/2)} = x+(-a) ==>

Dual[ m(r,0) = f(x) ] = { < k+a,( k^{2}+(-1)·(k+a)^{2} )^{(1/2)} > }

Teorema:

Sea m(r,0) = ( |x|^{2}+|y|^{2} )^{(1/2)} = x^{2}+(-a) ==>

Dual[ m(r,0) = f(x) ] = { < k^{(1/2)·[1:a]},( k^{2}+(-1)·k^{[1:a]} )^{(1/2)} > }

Series de Riemann-Ramanujan:

Arte:

[Ek][ sum[n = 1]-[oo][ ( 1/(2k)! )·(1/n)^{2k}·(4k+(-2)) ] = (1/6)·pi^{2} ]

Exposición:

k = 1

f(2k) = 2

sum[n = 1]-[oo][ ( 1/(2k)! )·(1/n)^{2}·(2·(2k)+(-2)) ] = ...

... sum[n = 1]-[oo][ ( 1/(f(2k))! )·(1/n)^{f(2k)}·(2·f(2k)+(-2)) ] = ...

... sum[n = 1]-[oo][ (1/2!)·(1/n)^{2}·(4+(-2)) ] = sum[n = 1]-[oo][ (1/2)·(1/n)^{2}·2 ] = ...

... sum[n = 1]-[oo][ (1/n)^{2} ] = (1/6)·pi^{2}

Arte:

[Ek][ sum[n = 1]-[oo][ ( 1/(3k)! )·(1/n)^{3k}·(9k+(-3)) ] = (1/24)·pi^{3} ]

Arte:

[Ek][ sum[n = 1]-[oo][ ( (4k+(-2))/(4k)! )·(1/n)^{4k}·(16k+(-4)) ] = (1/90)·pi^{4} ]

Arte:

[Ek][ sum[n = 1]-[oo][ ( (5k+1)/(5k)! )·(1/n)^{5k}·(25k+(-5)) ] = (1/300)·pi^{5} ]

geometría-diferencial y arte-matemático y números-y-vectores-afines y evangelio-stronikiano y análisis-matemático y topología

Teorema:

Sea H_{kk}^{k} = k ==> 

x_{k}(t) = (1/k)·ln(t)

Si d_{t}[x_{s}]^{2} = ( x_{s} )^{2} ==>

x_{s}(t) = e^{t}

R_{ijs}^{sss} = ij·t^{2}·e^{2t}

Teorema:

Sea H_{kk}^{k} = k ==> 

x_{k}(t) = (1/k)·ln(t)

Si d_{t}[x_{s}] = x_{s} ==>

x_{s}(t) = e^{t}

R_{ssk}^{sss} = kt·e^{t}

Teorema:

Sea H_{kk}^{k} = kt ==> 

x_{k}(t) = (2/k)·(-1)·(1/t)

Si d_{t}[x_{s}]^{2} = ( x_{s} )^{n} ==>

x_{s}(t) = ( (1+(-1)·(1/2)·n)·t )^{( 1/(1+(-1)·(1/2)·n) )}

R_{ijs}^{sss} = ij·(1/4)·t^{4}·( (1+(-1)·(1/2)·n)·t )^{( n/(1+(-1)·(1/2)·n) )}

Teorema:

Sea H_{kk}^{k} = kt ==> 

x_{k}(t) = (2/k)·(-1)·(1/t)

Si d_{t}[x_{s}] = ( x_{s} )^{n} ==>

x_{s}(t) = ( (1+(-n))·t )^{( 1/(1+(-n)) )}

R_{ssk}^{sss} = k·(1/2)·t^{2}·( (1+(-n))·t )^{( n/(1+(-n)) )}

Arte:

[En][ sum[k = 1]-[n][ mcd{km,k} ] = n ]

Exposición:

n = 1

f(k) = 1

sum[k = 1]-[n][ mcd{km,k} ] = sum[k = 1]-[n][ mcd{f(k)·m,f(k)} ] = ...

... sum[k = 1]-[n][ mcd{m,1} ] = sum[k = 1]-[n][ 1 ] = n

Arte:

[En][ sum[k = 1]-[n][ mcm{km,k} ] = nm ]

Exposición:

n = 1

f(k) = 1

sum[k = 1]-[n][ mcm{km,k} ] = sum[k = 1]-[n][ mcm{f(k)·m,f(k)} ] = ...

... sum[k = 1]-[n][ mcm{m,1} ] = sum[k = 1]-[n][ m ] = nm

Examen:

Arte:

[En][ sum[k = 1]-[n][ mcd{m+k,m} ] = n ]

Arte:

[En][ sum[k = 1]-[n][ mcm{m^{k},m} ] = nm ]

Definición: [ de número afín ]

Sea ( r € Q & m € Z & k € Z ) ==>

{ mk : r } = mk+[r] & [Ej][ j € Z & [r] = jr ]

Teorema:

[(-r)]+r = 0

Demostración:

[(-r)]+r = j·(-r)+r

Sea j = 1 ==>

[(-r)]+r = (-r)+r = 0

Teorema:

{ mk : 0 } = mk

Demostración:

{ mk : 0 } = mk+[0] = mk+0j = mk

Teorema:

a·[r] = [ar]

a·{ mk : r } = a·mk+[r]

Demostración:

a·[r] = a·(jr) = (aj)·r = (ja)·r = j·(ar) = [ar]

a·{ mk : r } = a·mk+a·[r] = a·mk+a·(jr) = a·mk+(aj)·r = a·mk+wr = a·mk+[r]

Definición: [ de múltiplo de un número afín ]

f(k) =[m]= g(j) <==> ...

... a·{ mk : r }+(-b)·{ mj : r } = m·( ak+(-1)·bj )

Definición: [ de potencia de un número afín ]

Sea ( { mk : r } )^{p} = { (mk)^{p} : r } ==>

f(k) =[m]= g(j) <==> ...

... ( { mk : r } )^{p}+(-1)·( { mj : r } )^{q} = m·( k^{p}·m^{p+(-1)}+(-1)·j^{q}·m^{q+(-1)} )

Teorema:

ax^{n}+b =[m]= 0 <==> x = { mk : (-b) }

Demostración:

a·{ mk : (-b) }^{n}+b = a·{ (mk)^{n} : (-b) }+b = ( a·(mk)^{n}+[(-b)] )+b = ...

... a·(mk)^{n}+([(-b)]+b) = a·(mk)^{n}+0 = a·(mk)^{n} =[m]= 0

Teorema:

Sea [Aj][ 1 [< j [< n ==> a_{j} != 0 ] ==>

a_{n}·x^{n}+...+a_{1}·x+a_{0} =[m]= 0 <==> x = { mk : (-1)·(1/n)·a_{0} }

Demostración:

sum[j = 1]-[n][ a_{j}·( { mk : (-1)·(1/n)·a_{0} } )^{j} ]+a_{0} = ...

... sum[j = 1]-[n][ a_{j}·( { (mk)^{j} : (-1)·(1/n)·a_{0} } ]+a_{0} = ...

... sum[j = 1]-[n][ a_{j}·(mk)^{j}+[(-1)·(1/n)·a_{0}] ]+a_{0} = ...

... sum[j = 1]-[n][ a_{j}·(mk)^{j}+(1/n)·[(-1)·a_{0}] ]+a_{0} = ...

... ( sum[j = 1]-[n][ a_{j}·(mk)^{j} ]+[(-1)·a_{0}]+a_{0} = ...

... sum[j = 1]-[n][ a_{j}·(mk)^{j} ]+( [(-1)·a_{0}]+a_{0} ) = ...

... sum[j = 1]-[n][ a_{j}·(mk)^{j} ]+0 = sum[j = 1]-[n][ a_{j}·(mk)^{j} ] =[m]= 0

Definición: [ de vector afín ]

Sea ( r € E & v € E & k € R ) ==>

{ kv : r } = kv+[r] & [EB][ B es matriz & [r] = (B o r) ]

Teorema:

[(-r)]+r = 0

Demostración:

[(-r)]+r = (B o (-r))+r

Sea B = Id ==>

[(-r)]+r = (Id o (-r))+r = (-r)+r = 0

Teorema:

{ kv : 0 } = kv

Demostración:

{ kv : 0 } = kv+[0] = kv+(B o 0) = kv+0 = kv

Teorema:

A o { kv : r } = k·(A o v)+[r] ==>

Demostración:

A o { kv : r } = k·(A o v)+A o [r] = k·(A o v)+A o (B o r) = k·(A o v)+(A o B ) o r = ...

... k·(A o v)+(C o r) = k·(A o v)+[r]

Definición: [ de producto de matrices de un vector afín ]

f(k) =[H(v)]= g(j) <==> ...

... A o { kv : r }+(-1)·( B o { jv : r } ) = ( k·A+(-1)·j·B ) o v

Ley: [ primera de condenación del Mal ]

Rezar al próximo,

sin Ley del Talión,

no se condena el Mal

odiando al próximo no como a si mismo 

pero es destrucción.

Quizás rezar al prójimo,

con Ley del Talión,

no se condena el Mal,

odiando al prójimo como a si mismo 

y entonces también no es destrucción.

Ley: [ segunda de condenación del Mal ]

Rezar al próximo,

con Ley del Talión,

se condena el Mal,

odiando al próximo como a si mismo

pero es destrucción. 

Quizás rezar al prójimo,

sin Ley del Talión,

se condena el Mal,

odiando al prójimo no como a si mismo

y entonces también no es destrucción.

Ley:

Con Ley del Talión rezando al prójimo,

hay condenación,

no teniendo-la el Mal

porque por igualdad tiene alguien la condenación. 

Sin Ley del Talión rezando al prójimo,

no hay condenación,

teniendo-la el Mal

aunque quizás por igualdad tiene alguien la condenación. 

Teorema:

Sea ( f(x) expansiva & d_{x}[f(x)] creciente ) ==>

Si f(0) = 0 ==> [Ax][ 0 < x·d_{x}[f(x)] < 1 ==> d_{x}[f(x)] >] (1/x)·ln(1+x) ]

Demostración:

0 [< c [< x

e^{x·d_{x}[f(x)]} >] 1+x·d_{x}[f(x)] >] 1+x·d_{x}[f(c)] = 1+f(x) >] 1+x

Teorema:

Sea ( f(x) expansiva & d_{x}[f(x)] creciente ) ==>

Si f(0) = 0 ==> [Ax][ 0 < x·d_{x}[f(x)] < 1 ==> d_{x}[f(x)] >] (1/x)·arc-sinh(x) ]

Demostración:

0 [< c [< x

sinh( x·d_{x}[f(x)] ) >] x·d_{x}[f(x)] >] x·d_{x}[f(c)] = f(x) >] x

Teorema:

Sea H(x) = ( f(x) )^{n} & d_{x}[f(x)] creciente ) ==>

Si f(0) = 0 ==> [Ax][ x > 0 ==> d_{x}[H(x)] >] (n/x)·H(x) ]

Demostración:

0 [< c [< x

d_{x}[H(x)] = d_{x}[ ( f(x) )^{n} ] = n·( f(x) )^{n+(-1)}·d_{x}[f(x)] >] ...

... n·( f(x) )^{n+(-1)}·d_{x}[f(c)] = n·( f(x) )^{n+(-1)}·(f(x)/x) = (n/x)·H(x)

Teorema:

Sea H(x) = e^{n·f(x)} & d_{x}[f(x)] creciente & [Ek][Ax][ x >] k ==> f(x) expansiva ] ) ==>

Si f(0) = 0 ==> [Ax][ x >] k ==> d_{x}[H(x)] >] n·H(x) ]

Demostración:

0 [< c [< x

d_{x}[H(x)] = d_{x}[ e^{n·f(x)} ] = n·e^{n·f(x)}·d_{x}[f(x)] >] ...

... n·e^{n·f(x)}·d_{x}[f(c)] = n·e^{n·f(x)}·(f(x)/x) >] n·e^{n·f(x)}·(x/x) = n·H(x)

Teoremas de Cámara-Garriga:

Teorema:

Sea A_{k} [<< A_{k+1} ==>

sum[k = 1]-[n][ [ || ]-[i = 1]-[k][ A_{i} ] ] = [ || ]-[k = 1]-[n][ sum[i = 1]-[k][ A_{i} ] ]

Sea A_{k} >>] A_{k+1} ==>

sum[k = 1]-[n][ [&]-[i = 1]-[k][ A_{i} ] ] = [ || ]-[k = 1]-[n][ sum[i = 1]-[k][ A_{i} ] ]

Demostración:

Sea A_{k} [<< A_{k+1} ==>

sum[k = 1]-[n][ [ || ]-[i = 1]-[k][ A_{i} ] ] = ...

... [ || ]-[i = 1]-[1][ A_{i} ]+...+[ || ]-[i = 1]-[n][ A_{i} ] = A_{1}+...+A_{n}

[ || ]-[k = 1]-[n][ sum[i = 1]-[k][ A_{i} ] ] = sum[i = 1]-[n][ A_{i} ] = A_{1}+...+A_{n}

Teorema:

Sea ¬A_{k} >>] ¬A_{k+1} ==>

sum[k = 1]-[n][ [&]-[i = 1]-[k][ ¬A_{i} ] ] = [&]-[k = 1]-[n][ sum[i = 1]-[k][ ¬A_{i} ] ]

Sea ¬A_{k} [<< ¬A_{k+1} ==>

sum[k = 1]-[n][ [ || ]-[i = 1]-[k][ ¬A_{i} ] ] = [&]-[k = 1]-[n][ sum[i = 1]-[k][ ¬A_{i} ] ]

Teorema:

Sea ( h(0) = 0 & h(i) creciente ) ==>

Si E_{i} = { x : 0 [< x [< h(i) } ==> E_{i} está compactificada en m clases

Demostración:

A_{0} = {0}

A_{i+1} = E_{i+1} [ \ ] E_{i} = { x : h(i) < x [< h(i+1) }

Sea i = mk ==>

A_{mk+1} = E_{mk+1} [ \ ] E_{mk}

Sea i = mk+m ==>

A_{mp+1} = A_{m·(k+1)+1} = A_{(mk+m)+1} = E_{(mk+m)+1} [ \ ] E_{mk+m}

Teorema:

Sea ( h(0) = 0 & h(-i) decreciente ) ==>

Si E_{(-i)} = { x : h(-i) [< x [< 0 } ==> E_{(-i)} está compactificada en m clases

Demostración:

A_{0} = {0}

A_{(-i)+(-1)} = E_{(-i)+(-1)} [ \ ] E_{(-i)} = { x : h((-i)+(-1)) [< x < h(-i) }

Sea (-i) = (-m)·k ==>

A_{(-m)·k+(-1)} = E_{(-m)·k+(-1)} [ \ ] E_{(-m)·k}

Sea (-i) = (-m)·k+(-m) ==>

A_{(-m)·p+(-1)} = A_{(-m)·(k+1)+(-1)} = A_{( (-m)·k+(-m) )+(-1)} = ...

... E_{( (-m)·k+(-m) )+(-1)} [ \ ] E_{(-m)·k+(-m)}

Teorema:

Si E_{i} = { x : 0 [< x [< 2i } ==> E_{i} está compactificada en 4 clases

Demostración:

A_{0} = {0}

Sea i = 4k ==>

A_{4k+1} = E_{2·(2k+1)+(-1)} [ \ ] E_{2·(2k)}

Sea i = 4k+1 ==>

A_{4k+2} = E_{2·(2k+1)} [ \ ] E_{2·(2k+1)+(-1)}

Sea i = 4k+2 ==>

A_{4k+3} = E_{2·(2k+2)+(-1)} [ \ ] E_{2·(2k+1)}

Sea i = 4k+3 ==>

A_{4k+4} = E_{2·(2k+2} [ \ ] E_{2·(2k+2)+(-1)}

Sea i = 4k+5 ==>

A_{4p+1} = A_{4·(k+1)+1} = A_{(4k+4)+1} = E_{2·(2k+2)+1} [ \ ] E_{2·(2k+2)}

topología-algebraica y álgebra y métodos-numéricos y análisis-funcional y series-de-Fourier-y-constante-de-Áperi y arte-matemático

Definición:

B^{0} = O

B^{1} = B

B^{2} = BB

B^{n+2} = BO...(n)...OB

Teorema:

B^{n}·O = B^{n}

Demostración:

B^{n}·O = B^{n}·B^{0} = B^{n+0} = B^{n}

Teorema:

x^{2}+(-1)·BB = (x+B)·(x+(-B))

x^{2}+BB = (x+iB)·(x+(-i)·B)

Grupo suma y espacio vectorial:

Definición:

... a_{0}·O+a_{1}·B+sum[k = 0]-[n+(-1)][ a_{k+2}·BO...(k)...OB ] ...

... +...

... b_{0}·O+b_{1}·B+sum[k = 0]-[n+(-1)][ b_{k+2}·BO...(k)...OB ] = ...

... (a_{0}+b_{0})·O+(a_{1}+b_{1})·B+sum[k = 0]-[n+(-1)][ (a_{k+2}+b_{k+2})·BO...(k)...OB ]

Definición:

w·( a_{0}·O+a_{1}·B+sum[k = 0]-[n+(-1)][ a_{k+2}·BO...(k)...OB ] ) =...

... (w·a_{0})·O+(w·a_{1})·B+sum[k = 0]-[n+(-1)][ (w·a_{k+2})·BO...(k)...OB ]

Grupo producto por coordenada:

Definición:

... a_{0}·O+a_{1}·B+sum[k = 0]-[n+(-1)][ a_{k+2}·BO...(k)...OB ] ...

... [+ · +] ...

... b_{0}·O+b_{1}·B+sum[k = 0]-[n+(-1)][ b_{k+2}·BO...(k)...OB ] = ...

... (a_{0}·b_{0})·O+(a_{1}·b_{1})·B+sum[k = 0]-[n+(-1)][ (a_{k+2}·b_{k+2})·BO...(k)...OB ]

Teorema:

< BOB+BB+B+O,BB+B+O,B+O,O > es base

Demostración:

Independencia lineal:

a·(BOB+BB+B+O)+b·(BB+B+O)+c·(B+O)+d·O = 0

a·BOB+(a+b)·(BB)+(a+b+c)·B+(a+b+c+d)·O = 0

a = 0

a = 0 & b = 0

a = 0 & b = 0 & c = 0

a = 0 & b = 0 & c = 0 & d = 0

Generador:

a·BOB+b·BB+c·B+d·O = a·(BOB+BB+B+O)+(b+(-a))·(BB+B+O)+(c+(-b))·(B+O)+(d+(-c))·O

Definición:

[Ev][ F(x) = x+v ]

Teorema:

F(x+y) = F(x)+F(y)

F(w·x) = w·F(x)

Demostración:

F(x+y) = (x+y)+v = (x+y)+( (1/2)·v+(1/2)·v ) = (x+(1/2)·v)+(y+(1/2)·v) = (x+p)+(y+q) = F(x)+F(y)

F(w·x) = w·x+v = w·( x+(1/w)·v ) = w·(x+s) = w·F(x)

Teorema:

Ker(F) = {(-v)}

Demostración:

F(-v) = (-v)+v = 0

Teorema:

Si ( E/Ker(F) ) = {z+(-v)} ==> F[ ( E/Ker(f) ) ] = E

Demostración:

F(z+(-v)) = (z+(-v))+v = z+((-v)+v) = z+0 = z

Teorema:

Si ( E/Ker(F) ) = {z+(-v)} ==> Im(F) =[h(z)]= ( E/Ker(F) )

Demostración:

h(x) = h(y)

x+(-v) = y+(-v)

x = y

h(x+(-v)) = f(y+(-v))

x = y

x+(-v) = y+(-v)

Definición:

[Ev][ F(x,y) = xy+v ]

Teorema:

F(z,x+y) = F(z,x)+F(z,y)

F(z,w·x) = w·F(z,x)

Demostración:

F(z,x+y) = z·(x+y)+v = (zx+zy)+v = (zx+zy)+( (1/2)·v+(1/2)·v ) = (zx+(1/2)·v)+(zy+(1/2)·v) = ...

... (zx+p)+(zy+q) = F(z,x)+F(z,y)

F(z,w·x) = z·(w·x)+v = w·(zx)+v = w·( zx+(1/w)·v ) = w·(zx+s) = w·F(z,x)

Teorema:

Ker(F) = { < z,(1/z)·(-v) > || < (-v)·(1/z),z > }

Demostración:

F(z,(1/z)·(-v)) = z·((1/z)·(-v))+v = (z/z)·(-v)+v = (-v)+v = 0

Teorema:

Si ( E/Ker(F) ) = { < z,(1/z)·(-v)+s > || < (-v)·(1/z)+s,z > } ==> Im(F) =[h(w)]= ( E/Ker(F) )

Demostración:

h(z,(1/z)·(-v)+p) = h(z,(1/z)·(-v)+q)

zp = zq

p = q

(1/z)·(-v)+p = (1/z)·(-v)+q

< z,(1/z)·(-v)+p > = < z,(1/z)·(-v)+q >

h(zp) = h(zq)

< z,(1/z)·(-v)+p > = < z,(1/z)·(-v)+q >

(1/z)·(-v)+p = (1/z)·(-v)+q

p = q

zp = zq

Teorema:

Sea F(x,y) = xy+BB ==>

Ker(F) = { < B^{n},(O/B)^{n}·(-1)·BB > || < (-1)·BB·(O/B)^{n},B^{n} > }

Teorema:

Si d_{t}[z] = f(t)·z ==> z_{n}(t) = z_{0}·( 1+h·f(t) )^{n}

Si h = 0·( int[f(t)]d[t]/f(t) ) ==> 

... z_{n}(t) = ( 1+0·int[f(t)]d[t] )^{n}

Método numérico convergente:

(1/h)·( z_{n+1}+(-1)·z_{n} ) = f(t)·z_{n}

z_{0} = 1

Demostración:

(1/h)·( z_{n+1}+(-1)·z_{n} ) = f(t)·z_{n}

( z_{n+1}+(-1)·z_{n} ) = h·f(t)·z_{n}

z_{n+1} = z_{n}+h·f(t)·z_{n}

z_{n+1} = z_{n}·(1+h·f(t))

Teorema:

Si d_{t}[z] = f(t)·(1/z) ==> a_{n}(t) = a_{0}+(n/2)·h·f(t)

Si h = (1/n) ==> 

... a(t) = a_{0}+(1/2)·f(t)

... z(t) = ( 2a_{0}+f(t) )^{(1/2)} & a_{0} = int[f(t)]d[t]+(-1)·(1/2)·f(t)

Método numérico convergente:

(1/h)·( z_{n+1}+(-1)·z_{n} ) = ( f(t)/z_{n} )

z_{0} = ( 2·int[f(t)]d[t]+(-1)·f(t) )^{(1/2)}

Demostración:

(1/h)·( z_{n+1}+(-1)·z_{n} ) = ( f(t)/z_{n} )

( z_{n+1}+(-1)·z_{n} ) = ( (h·f(t))/z_{n} )

z_{n+1} = z_{n}+( (h·f(t))/z_{n} )

z_{n+1}·z_{n} = ( z_{n} )^{2}+h·f(t)

Sea z_{n} = ( 2a_{n} )^{(1/2)} &  z_{n+1}·z_{n} = 2a_{n+1} ==>

2a_{n+1} = 2a_{n}+h·f(t)

a_{n+1} = a_{n}+(1/2)·h·f(t)

Teorema:

Forma integral interior:

Sea F(ax+b) = int[x = 0]-[1][ ax+b ]d[x] ==>

G(ax+b) = int[x = 0]-[1][ (8/a)·x+(-1)·(1/b) ]d[x]

F(ax+b) [o] G(ax+b) = 1

Teorema:

Forma integral exterior:

Sea F(ax+b) = int[x = 0]-[1][ ax+b ]d[x] ==>

G(ax+b) = int[x = 0]-[1][ (4/a)·x+(-1)·(1/b) ]d[x]

F(ax+b) [o] G(ax+b) = 0

Teorema:

Forma funcional interior:

Sea F(h(x)) = sum[k = 1]-[n][ ( h(x) )^{k} ]+1 ==>

G(h(x)) = sum[k = 1]-[n][ (1/h(x))^{k} ]+((-n)+1)

F(h(x)) [o] G(h(x)) = 1

Teorema:

Forma funcional exterior:

Sea F(h(x)) = sum[k = 1]-[n][ ( h(x) )^{k} ]+1 ==>

G(h(x)) = sum[k = 1]-[n][ (1/h(x))^{k} ]+(-n)

F(h(x)) [o] G(h(x)) = 0

Teorema:

< cosh(kx), sinh(kx) > es linealmente independiente

Demostración

a·cosh(kx)+b·sinh(kx) = 0

(1/2)·( (a+b)·e^{kx}+(a+(-b))·e^{(-k)·x} ) = 0

(-a) = b = a 

a = 0 & b = 0 

Teorema:

sum[k = 0]-[n][ a_{k}·e^{kx}] = sum[k = 0]-[n][ a_{k}·cosh(kx)+a_{k}·sinh(kx) ]

Teorema:

sum[k = 0]-[n][ a_{k}·e^{(-k)·x}] = sum[k = 0]-[n][ a_{k}·cosh(kx)+a_{k}·(-1)·sinh(kx) ]

Teorema:

sum[k = 0]-[n][ a_{k}·e^{kxi}] = sum[k = 0]-[n][ a_{k}·cosh(kxi)+a_{k}·(1/i)·sinh(kxi) ]

Teorema:

sum[k = 0]-[n][ a_{k}·e^{(-k)·xi}] = sum[k = 0]-[n][ a_{k}·cosh(kx)+a_{k}·i·sinh(kxi) ]

Definición:

[Ex][ f_{sup{k}}(x) = c_{0}+sum[k = 1]-[oo][ a_{k}·cosh(x)+b_{k}·sinh(x) ] ]

c_{0} = (1/(2pi·i))·int[x = 0]-[2pi·i][ f_{1}(x) ]d[x]

a_{k} = (1/(pi·i))·int[x = 0]-[2pi·i][ f_{k}(x)·cosh(x) ]d[x]

b_{k} = (-1)·(1/(pi·i))·int[x = 0]-[2pi·i][ f_{k}(x)·sinh(x) ]d[x]

Axioma:

Si f_{k}(x) = (x/k)^{s} ==> sup{(1/k)} = max{s+(-1),1}

Teorema:

Sea f_{k}(x) = (x/k)^{n} ==>

Si n >] 4 ==> No es resoluble el método

Demostración:

Sea 0 [< j [< n ==>

x^{n+(-j)} = k^{n+(-j)}

Existen más de 5 puntos fijos

No es resoluble el método

Teorema:

Sea f_{k}(x) = kx ==>

(oo·x) = 2·0·sinh(x)·sum[k = 1]-[oo][ k ]

Sea x = 0 ==>

sum[k = 1]-[oo][ k ] = (1/2)·oo^{2}

Teorema:

Sea f_{k}(x) = (x/k) ==>

sup{(1/k)} = max{s+(-1),1} = max{(1+(-1)),1} = 1

x = 2·0·sinh(x)·sum[k = 1]-[oo][ (1/k) ]

Sea x = ln(oo) ==>

sum[k = 1]-[oo][ (1/k) ] = ln(oo)

Teorema:

Sea f_{k}(x) = (x/k)^{2} ==>

sup{(1/k)} = max{s+(-1),1} = max{(2+(-1)),1} = 1

x^{2} = (-1)·(8/3)·pi^{2}+(-1)·2·4·cosh(x)·sum[k = 1]-[oo][ (1/k)^{2} ]

Sea x = (2pi·i) ==>

sum[k = 1]-[oo][ (1/k)^{2} ] = (1/6)·pi^{2}

c_{0} = (1/(pi·i))·(1/3)·(2pi·i)^{3} = (-1)·(8/3)·pi^{2}

Teorema:

Sea f_{k}(x) = (x/k)^{3} ==>

sup{(1/k)} = max{s+(-1),1} = max{(3+(-1)),1} = 2

(2x)^{3} = (-1)·3·2·4·sinh(x)·sum[k = 1]-[oo][ (1/k)^{3} ]

Sea x = (pi/2)·i ==>

sum[k = 1]-[oo][ (1/k)^{3} ] = (1/24)·pi^{3}

Teorema:

Sea f_{k}(x) = (x/k)^{5 || ( 4 ==> 5 ) || ( 3 ==> 4 ) || ( 2 ==> 1 ) }} ==>

f_{k}(x) es resoluble

n = ( 5 || 4 || 1 || 0 )

sup{(1/k)} = max{s+(-1),1} = max{(5+(-1)),1} = 4

(4x)^{5} = (-1)·5·(4·(-5))·(3·(-4))·(2·(-1))·4·sinh(x)·sum[k = 1]-[oo][ (1/k)^{5} ]

Sea x = (pi/2)·i ==>

sum[k = 1]-[oo][ (1/k)^{5} ] = (1/300)·pi^{5}

Teorema:

f_{k}(x) = (x/k)^{7 || 7 ==> 7 || 6 ==> 45 || 5 ==> 45 || 4 ==> 4 || 3 ==> 9 || 2 ==> 2 }

f_{k}(x) es resoluble

n = ( 45 || 9 || 1 || 0 )

sup{(1/k)} = max{s+(-1),1} = max{(7+(-1)),1} = 6

(6x)^{7} = ...

... (-1)·(7/(-7))·(6·(-45))·(5·(-45))·(4/(-4))·(3·(-9))·(2/(-2))·4·sinh(x)·sum[k = 1]-[oo][ (1/k)^{7} ]

Sea x = (pi/2)·i ==>

sum[k = 1]-[oo][ (1/k)^{7} ] = (1/3,000)·pi^{7}

Principio del Mal:

Rezar al próximo,

sin condenación instantánea,

no amando al próximo como a ti mismo.

Rezar al prójimo,

con condenación instantánea,

amando al prójimo como a ti mismo.

Ley:

Rezar al Mal proyectado le pasa al cuerpo del próximo:

de cuerpo del próximo semejante al próximo,

no amando al próximo como a ti mismo.

Rezar al Mal proyectado no le pasa al cuerpo del prójimo:

de alma del próximo semejante al prójimo,

amando al prójimo como a ti mismo.

Arte: [ de serie de Laurent ]

[En][ d_{a...a}^{n}[f(a)] = (-1)^{n}·(n+(-1))!·d_{a...a}^{n}[f(a)] ]

Exposición:

n = 2

f(1) = (1/n)

g(1/n) = 0

H(1) = z

[o(1)o] = [o(H(1))o] = [o(z)o]

r = 0 & z = re^{x}+a

d_{z...z}^{n+1}[f(z)] = d_{z}^{1}[ d_{z...z}^{n}[f(z)] ] = d_{z}^{f(1)}[ d_{z...z}^{n}[f(z)] ] = ...

... d_{z}^{(1/n)}[ d_{z...z}^{n}[f(z)] ] = d_{z}^{g(1/n)}[ d_{z...z}^{n}[f(z)] ] = ...

... d_{z}^{0}[ d_{z...z}^{n}[f(z)] ] = d_{z...z}^{n}[f(z)]

Por inducción:

d_{z...z}^{n}[f(z)] = (-1)^{n}·(n+(-1))!·d_{z...z}^{n}[f(z)] = ...

... int-...(n)...-int[x = 0]-[1][z = re^{x}+a][ ...

... (n+(-1))!·d_{z...z}^{n}[f(z)]·(1/(a+(-z))^{n})·d[z]...(n)...d[z] = ...

... int-...(n+1)...-int[x = 0]-[1][z = re^{x}+a][ ...

... (n+(-1))!·d_{z}[ d_{z...z}^{n}[f(z)]·(1/(a+(-z))^{n}) ]·d[z]...(n+1)...d[z] = ...

... int-...(n+1)...-int[x = 0]-[1][z = re^{x}+a][ ...

... (n+(-1))!·d_{z}[ d_{z...z}^{n}[f(z)] [o(z)o] (1/(a+(-z))^{n}) ]·d[z]...(n+1)...d[z] = ...

... int-...(n+1)...-int[x = 0]-[1][z = re^{x}+a][ ...

... n!·d_{z...z}^{n+1}[f(z)]·(1/(a+(-z))^{n+1})·d[z]...(n+1)...d[z] = (-1)^{n+1}·n!·d_{z...z}^{n+1}[f(z)]

Arte:

[Ex][ e^{x} = 1+sum[k = 1]-[oo][ (-1)^{n}·(1/n)·x^{n} ] ]

[Ex][ e^{(-x)} = 1+sum[k = 1]-[oo][ (1/n)·x^{n} ] ]

Arte: [ de falsus infinitorum ]

sum[k = 1]-[oo][ ( ln(1+k) )^{k} ] != ln(2)

sum[k = 1]-[oo][ ( ln(1+(1/k)) )^{k} ] != ln(2)

Exposición:

Sea n = 1 ==>

sum[k = 1]-[n][ ( ln(1+k) )^{k} ] = ln(2)

f(k) = 1

g(1) = n

sum[k = 1]-[n][ ( ln(1+k) )^{k} ] = sum[k = 1]-[n][ (1/g(1))·( ln(1+f(k)) )^{f(k)} ] = ...

... sum[k = 1]-[n][ (1/n)·ln(2) ] = ln(2)

Sea n = oo ==>

sum[k = 1]-[n][ ( ln(1+k) )^{k} ] = ln(2)

Arte: [ de falsus infinitorum ]

sum[k = 1]-[oo][ ln(1+k)+(-1)·(1/k) ] != ln(2)

sum[k = 1]-[oo][ ln(1+(1/k))+(-1)·(1/k) ] != ln(2)

Exposición:

Sea n = 1 ==>

sum[k = 1]-[n][ ln(1+k)+(-1)·(1/k) ]+(1/n) = ln(2)

f(k) = 1

sum[k = 1]-[n][ ln(1+k)+(-1)·(1/k) ]+(1/n) = sum[k = 1]-[n][ ln(1+f(k))+(-1)·(1/k) ]+(1/n) = ...

... sum[k = 1]-[n][ ln(2)+(-1)·(1/k) ]+(1/n)

Sea n = oo ==>

sum[k = 1]-[oo][ ln(1+k)+(-1)·(1/k) ] = sum[k = 1]-[oo][ ln(1+k)+(-1)·(1/k) ]+(1/oo) = ...

... sum[k = 1]-[oo][ ln(2)+(-1)·(1/k) ]+(1/oo) = sum[k = 1]-[oo][ ln(2)+(-1)·(1/k) ] = ...

... ln(2)·oo+(-1)·ln(oo) = ln(2)·oo+(-1)·ln(2)·oo = ln(2)

formas-diferenciales-aplicadas-a-la-física y geometría-diferencial y topología y cinemática-física y análisis-matemático

Principio: [ de súper-conducción de electrones coherentes ]

H(x,y,t) = int-int[ sin(ut)·f(ax)·d[ut]-[&]-d[ax]+cos(ut)·g(ay)·d[ut]-[&]-d[ay] ] 

T·( (-1)·cos(ut)·F(ax)+sin(ut)·G(ay) [o] H(x,y,t) ) = T+(-1)·T_{0}

Principio: [ de súper-conducción de gravitones coherentes ]

H(x,y,t) = int-int[ sinh(ut)·f(ax)·d[ut]-[&]-d[ax]+(1/i)·cosh(ut)·g(ay)·d[ut]-[&]-d[ay] ] 

T·( cosh(ut)·F(ax)+(1/i)·sinh(ut)·G(ay) [o] H(x,y,t) ) = T+(-1)·T_{0}

Principio: [ de láser de fotones eléctricos coherentes ]

H(x,y,t) = int-int[ e^{uti}·f(ax)·d[uti]-[&]-d[ax]+e^{(-1)·uti}·g(ay)·d[uti]-[&]-d[ay] ] 

z·( e^{uti}·F(ax)+(-1)·e^{(-1)·uti}·G(ay) [o] H(x,y,t) ) = z+(-1)·z_{0}

Principio: [ de láser de fotones gravitatorios coherentes ]

H(x,y,t) = int-int[ e^{ut}·f(ax)·d[ut]-[&]-d[ax]+e^{(-1)·ut}·g(ay)·d[ut]-[&]-d[ay] ] 

z·( e^{ut}·F(ax)+(-1)·e^{(-1)·ut}·G(ay) [o] H(x,y,t) ) = z+(-1)·z_{0}

Principio: [ de estabilizador de carga de electrones ]

H(x,y,t) = int-int[ sin(ut)·f(ax)·d[ut]-[ || ]-d[ax]+cos(ut)·g(ay)·d[ut]-[ || ]-d[ay] ] 

q·( (-1)·cos(ut)·F(ax)+sin(ut)·G(ay) [o] H(x,y,t) ) = 2q+(-1)·q_{0}

H(x,y,t) = (-1)·cos(ut)·(1/F(ax))+sin(ut)·(1/G(ay))

Principio: [ de estabilizador de carga de gravitones ]

H(x,y,t) = int-int[ sinh(ut)·f(ax)·d[ut]-[ || ]-d[ax]+(1/i)·cosh(ut)·g(ay)·d[ut]-[ || ]-d[ay] ] 

p·( cosh(ut)·F(ax)+(1/i)·sinh(ut)·G(ay) [o] H(x,y,t) ) = 2p+(-1)·p_{0}

H(x,y,t) = cosh(ut)·(1/F(ax))+(1/i)·sinh(ut)·(1/G(ay))

Anexo:

El estabilizador de conducción,

es un chip de diagonal-hipérbola y semi-círculo y hipérbola-diagonal.

Principio: [ de estabilizador de rotación de corriente eléctrico ]

H(x,y,t) = int-int[ sin(ut)·f(ax)·d[ut]-[ || ]-d[ax]+cos(ut)·g(ay)·d[ut]-[ || ]-d[ay] ] 

v·( (-1)·cos(ut)·F(ax)+sin(ut)·G(ay) [o] H(x,y,t) ) = 2v+(-1)·v_{0}

H(x,y,t) = (-1)·cos(ut)·(1/F(ax))+sin(ut)·(1/G(ay))

Principio: [ de estabilizador de rotación de corriente gravitatorio ]

H(x,y,t) = int-int[ sinh(ut)·f(ax)·d[ut]-[ || ]-d[ax]+(1/i)·cosh(ut)·g(ay)·d[ut]-[ || ]-d[ay] ] 

v·( cosh(ut)·F(ax)+(1/i)·sinh(ut)·G(ay) [o] H(x,y,t) ) = 2v+(-1)·v_{0}

H(x,y,t) = cosh(ut)·(1/F(ax))+(1/i)·sinh(ut)·(1/G(ay))

Anexo:

El estabilizador de rotación,

es un mecanismo donde circula un corriente,

de diagonal-hipérbola y semi-circulo y hipérbola-diagonal.

Teorema:

int-int[ z^{2n+(-1)}·d[y]-[&]-d[z]+z^{2n+(-1)}·d[z]-[&]-d[x]+(-1)·d[x]-[&]-d[y] ] = ...

... nx+ny+z^{2n}

Teorema:

int-int[ e^{2nz}·d[y]-[&]-d[z]+e^{2nz}·d[z]-[&]-d[x]+(-1)·d[x]-[&]-d[y] ] = ...

... nx+ny+e^{2nz}

Teorema:

int-int[ z^{3n+(-1)}·d[y]-[ || ]-d[z]+x^{3n+(-1)}·d[z]-[ || ]-d[x]+y^{3n+(-1)}·d[x]-[ || ]-d[y] ] = ...

... (1/z)^{3n}·(n/y)+(1/x)^{3n}·(n/z)+(1/y)^{3n}·(n/x)

Teorema:

int-int[ e^{3nz}·d[y]-[ || ]-d[z]+e^{3nx}·d[z]-[ || ]-d[x]+e^{3ny}·d[x]-[ || ]-d[y] ] = ...

... e^{(-3)·nz}·(n/y)+e^{(-3)·nx}·(n/z)+e^{(-3)·ny}·(n/x)

Geodésicas y Símbolos de Cristoffel:

Teorema:

Sea d_{tt}^{2}[x_{k}]+H_{ij}^{k}·d_{t}[x_{i}]·d_{t}[x_{j}] = 0 ==>

Si H_{kk}^{k} = d_{t}[ f_{k}(t) ] ==> x_{k}(t) = ( t /o(t)o/ int[ f_{k}(t) ]d[t] )

H_{ij}^{k} = ( 1/f_{k}(t) )^{2}·d_{t}[ f_{k}(t) ]·f_{i}(t)·f_{j}(t)

Demostración:

(-1)·( 1/d_{t}[x_{k}] )^{2}·d_{tt}^{2}[x_{k}] = H_{kk}^{k} = d_{t}[ f_{k}(t) ]

( 1/d_{t}[x_{k}] ) = f_{k}(t)

( 1/f_{k}(t) ) = d_{t}[x_{k}]

x_{k}(t) = ( t /o(t)o/ int[ f_{k}(t) ]d[t] )

Teorema:

Sea d_{tt}^{2}[x_{k}]+H_{ij}^{k}·d_{t}[x_{i}]·d_{t}[x_{j}] = 0 ==>

Si H_{kk}^{k} = k ==> x_{k}(t) = (1/k)·ln(t)

H_{ij}^{k} = (1/k)·ij

Demostración:

(-1)·( 1/d_{t}[x_{k}] )^{2}·d_{tt}^{2}[x_{k}] = H_{kk}^{k} = k

( 1/d_{t}[x_{k}] ) = kt

(1/(kt)) = d_{t}[x_{k}]

x_{k}(t) = (1/k)·ln(t)

Teorema:

Sea d_{tt}^{2}[x_{k}]+H_{ij}^{k}·d_{t}[x_{i}]·d_{t}[x_{j}] = 0 ==>

Si H_{kk}^{k} = e^{kt} ==> x_{k}(t) = (-1)·e^{(-1)·kt}

H_{ij}^{k} = k^{2}·e^{(-1)·kt}·(1/(ij))·e^{it+jt}

Teorema:

Sea d_{tt}^{2}[x_{k}]+H_{ij}^{k}·d_{t}[x_{i}]·d_{t}[x_{j}] = 0 ==>

Si H_{kk}^{k} = t^{k} ==> x_{k}(t) = (-1)·( (k+1)/k )·t^{(-k)}

H_{ij}^{k} = (k+1)^{2}·t^{(-k)+(-2)}·(1/(i+1))·(1/(j+1))·t^{i+1+j+1}

Teorema:

Si f(x) = x+s ==> f(x) es un morfismo topológico

Demostración:

f(max{x,y}) = max{x,y}+s = max{x+s,y+s} = max{f(x),f(y)}

x+s [< y+s

x [< y

max{x+s,y+s} = y+s = max{x,y}+s

Ley:

Si y(t) = (-1)·(1/2)·(q/m)·gt^{2}+h ==> d_{t}[y] = ( (q/m)·2g·(h+(-y)) )^{(1/2)}

Ley:

Si y(t) = (-1)·(1/6)·(I/m)·gt^{3}+h ==> d_{t}[y] = (1/2)·( (I/m)^{(1/2)}·6g^{(1/2)}·(h+(-y)) )^{(2/3)}

Teorema:

Sea Q(x) = f(t) ==>

A(x,t) = P(x)+(-1)·h(t)·x [o(x)o] ( Q(x)+(-1)·f(t) )

h(t) = ( d_{x}[P(x)]/d_{x}[Q(x)] )

Demostración: [ por doble destrocter ponens ]

Si Q(x_{k}) = f(t) ==> d_{k}[ Q(x_{k})+(-1)·f(t) ] = d_{k}[ Q(x_{k}) ]

Si [EF][ F(x_{k}) = f(t) ] ==> [AF][ F(x_{k}) != f(t) ]

Estando en la falsedad.

Si [AG][ G(x_{k}) != h(t) ] ==> [EG][ G(x_{k}) = h(t) ]

Estando en la verdad.

Teorema:

Sea x = f(t) ==>

F(x,t) = x^{n+1}+(-1)·h(t)·x [o(x)o] ( x+(-1)·f(t) )

h(t) = (n+1)·( f(t) )^{n}

Teorema:

Sea x^{m} = f(t) ==>

F(x,t) = x^{n+1}+(-1)·h(t)·x [o(x)o] ( x^{m}+(-1)·f(t) )

h(t) = ( (n+1)/m )·( f(t) )^{( (n+1)/m )+(-1)}

Teorema:

int[ sum[k = 1]-[n][ x_{1}·...d_{t}[x_{k}]·...·x_{n}·d[t] ] ] = n·x_{1}·...·x_{n}

Demostración: [ por doble destrocter ponens ]

Si [En][ x_{n+1} = 1 ] ==> [An][ x_{n+1} != 1 ]

Estando en la falsedad.

Si [An][ n != n+1 ] ==> [En][ n = n+1 ]

Estando en la verdad.

int[ sum[k = 1]-[n+1][ x_{1}·...d_{t}[x_{k}]·...·x_{n+1}·d[t] ] ] = ...

int[ sum[k = 1]-[n][ x_{1}·...d_{t}[x_{k}]·...·x_{n}·d[t] ] ] = n·x_{1}·...·x_{n} = ...

n·x_{1}·...·x_{n}·x_{n+1} = (n+1)·x_{1}·...·x_{n}·x_{n+1}

Egipto y evangelio-stronikiano y ley y análisis-matemático y teoría-de-números y ecuaciones-diferenciales

Principio:

Existe Deu-Cron el Creador.

Existe Dea-Cron la Creadora

Ley:

Deu-Cron es mente,

y el universo negro es mental.

Dea-Cron es mente,

y el universo blanco es mental.

Ley:

Como arriba es abajo,

y el que es tiene cuerpo,

como el que no es.

Como abajo es arriba,

y el que no es tiene cuerpo,

como el que es.

Ley:

Como a dentro es a fuera,

y el que es tiene alma,

como el no condenado.

Como a fuera es a dentro,

y el no condenado tiene alma,

como el que es.

Ley:

Nada escapa a la Ley en la vida.

Deducción:

Seth mató a su hermano Osiris,

y Horus el hijo de Osiris mató a Seth,

por condenación de Luz verdadera,

siendo así porque perdió un ojo,

que es la lámpara de nuestro cuerpo.

Ley:

Nada escapa a la Ley en la muerte.

Deducción:

Existe la pluma de la verdad de Osiris,

que juzga si vas al Cielo Aaru.

Ley:

Si se tiene condenación

entonces se reencarna en un mundo antiguo.

Deducción:

El dios Sol Ra adoptó a Seth después de morir,

siendo Seth el dios del mal y reencarnar.

Ley:

Si no se tiene condenación 

entonces se va al Cielo Aaru mientras el mundo es antiguo.

Deducción:

Osiris coloca un biyección espectral de tu corazón y la pluma de la verdad,

en la balanza dual y juzga si vas al Cielo Aaru,

siendo la biyección de tu corazón ligero en tinieblas,

sin ninguna condenación.

Ley:

Se va con la familia al Cielo Aaru una vez muerto y aceptado en él.

Deducción:

Anubis reúne a tu familia,

y te acompaña hasta el Cielo Aaru.

Ley:

Se puede reencarnar con la familia de vuelta del Cielo Aaru.

Deducción:

Anubis reúne a tu familia,

y te acompaña desde el Cielo Aaru hasta nacer.

Ley:

Puede haber proto-ascensión después de la muerte.

Deducción:

Proto-ascensión de Osiris hecha por Isis.

Ley:

Puede no haber proto-ascensión después de la muerte.

Deducción:

No proto-ascensión de Horus hecha por Isis.

Druidas:

Beguining:

Raded = Ra = Raded Quetzaqualetchkán = Raded Viracotechkán

Oded = Osiris = Oded Quetzaqualetchkán = Oded Viracotechkán

Weened = Isis = Weened Quetzaqualetchkán = Weened Viracotechkán

Zhor = Horus = Zhor Quetzaqualetchkán = Zhor Viracotechkán

Gorked = Seth = Gorked Quetzaqualetchkán = Gorked Viracotechkán

Fryded = Anubis = Fryded Quetzaqualetchkán = Fryded Viracotechkán

Law:

Days of the week:

Moonday

Gorkensday

Weenensday

Zhorsday

Frydensday

Odensday

Sunday

Falsas indulgencias de la iglesia:

Juan:

A quien les perdonéis los pecados,

les serán perdonados.

A quien les retengáis los pecados,

les serán retenidos.

Estaba Pedro desnudo,

cometiendo adulterio de Maestro,

enseñando-le la picha,

y le dijo una falsedad Jesucristo.

Si no hubiese estado Pedro desnudo,

no cometiendo adulterio de Maestro,

no enseñando-le la picha,

no le hubiese dicho una falsedad Jesucristo.

Ley: [ de Indulgencia por confesión de regresión ]

A quienes les recordéis los pecados,

les serán perdonados,

cuando pague la condenación el señor,

con la confesión al cura de regresión.

A quienes les olvidéis los pecados,

les serán retenidos,

mientras no pague condenación el señor,

sin la confesión al cura de regresión.

Ley:

Herencia genética del pasado,

regresión con aceite de Marihuana.

Destructor por Destructor igual a Constructor,

pagando condenación de la confesión de las vidas pasadas.

Herencia genética del presente,

regresión con aceite de Hierba Luisa.

Constructor por Constructor igual a Constructor,

pagando condenación de la confesión de la vida presente.

Ley:

Se creen que pueden ser malos,

porque se creen la indulgencia,

y que los atacan los hombres,

y que no es condenación.

Cuando no pueden se malos,

porque no hay indulgencia,

y no los atacan los hombres,

y es condenación.

Ley:

Seguid la Ley,

con los fieles,

como la ha seguido él.

No sigáis la Ley,

con los infieles,

como no la ha seguido él.

Ley: [ de capellán stronikiano ]

Es predicador del evangelio,

el que no se sale del concubinato,

que es tocamiento consentido o Camel-Toe,

porque no se expone a adulterio

habiendo caminado 5 años,

sin saber a donde ir viendo a donde va,

teniendo el centro del sexo encendido.

No es predicador del evangelio,

el que se sale del concubinato,

que es no tocamiento consentido ni Camel-Toe,

porque se expone a adulterio

no habiendo caminado 5 años,

sin saber a donde ir viendo a donde va,

no teniendo el centro del sexo encendido.

Artículo:

Un cardenal puede ordenar a un policía,

detener a un pedófilo religioso católico,

con posible curación,

cerrando-lo 5 años,

obligado a caminar,

sin saber a donde ir viendo a donde va.

Un cardenal puede ordenar a un militar,

matar a un pedófilo religioso católico,

sin posible curación,

no cerrado 5 años,

no obligado a caminar,

sin saber a donde ir viendo a donde va.

Ley:

Va Pevrost y le dice a un catalán:

Espérit un moment.

Teorema:

Si a_{n} € { z : z = (1/n) } ==> a_{oo} es neutro en suma

Si a_{n} € { z : z = (1/n) } ==> a_{1} es neutro en producto

Teorema:

Si a_{n} € { z : z = 1+(-1)·(1/n) } ==> a_{1} es neutro en suma

Si a_{n} € { z : z = 1+(-1)·(1/n) } ==> a_{oo} es neutro en producto

Teorema:

Si a_{n} € { z : [As][ s > 0 ==> | z+(-1)·(1/n) | < s ] } ==> a_{oo} es neutro en suma

Si a_{n} € { z : [As][ s > 0 ==> | z+(-1)·(1/n) | < s ] } ==> a_{1} es neutro en producto

Demostración:

Sea s > 0 ==>

| z+(-1)·(1/n) | < s

0 [< | z+(-1)·(1/n) | [< 0

| z+(-1)·(1/n) | = 0

z+(-1)·(1/n) = 0

z = z+0 = z+( (-1)·(1/n)+(1/n) ) = ( z+(-1)·(1/n) )+(1/n) = 0+(1/n) = (1/n)

a_{n} = z = (1/n)

Sea n = oo ==>

a_{oo} = (1/oo) = 0

Sea n = 1 ==>

a_{1} = (1/1) = 1

Teorema:

Si a_{n} € { z : [As][ s > 0 ==> | z+(-1)+(1/n) | < s ] } ==> a_{1} es neutro en suma

Si a_{n} € { z : [As][ s > 0 ==> | z+(-1)+(1/n) | < s ] } ==> a_{oo} es neutro en producto

Teorema:

Si a_{n} € { z : [As][ s > 1 ==> 1 [< (z/n) < s ] } ==> a_{0} es neutro en suma

Si a_{n} € { z : [As][ s > 1 ==> 1 [< (z/n) < s ] } ==> a_{1} es neutro en producto

Ley:

Aceptar una inhabilitación del Senado,

es vivir,

fuera del sistema.

No aceptar una inhabilitación del Senado,

es morir,

dentro del sistema.

Teorema:

Sea a € R ==>

[As][ s > 0 ==> | a_{oo}+(-a) | < s ] <==> lim[n = oo][ a_{n} ] = a

Demostración:

Sea s > 0 ==>

| lim[n = oo][ a_{n} ]+(-a) | = | a_{oo}+(-a) | < s

| lim[n = oo][ a_{n} ]+(-a) | = 0

lim[n = oo][ a_{n} ]+(-a) = 0

lim[n = oo][ a_{n} ] = a

Teorema:

Sea a numerable ==>

[As][ s > 0 ==> | ( a_{oo}/a )+(-1) | < s ] <==> lim[n = oo][ a_{n} ] = a

Demostración:

Sea s > 0 ==>

| ( lim[n = oo][ a_{n} ]/a )+(-1) | = | ( a_{oo}/a )+(-1) | < s

| ( lim[n = oo][ a_{n} ]/a )+(-1) | = 0

( lim[n = oo][ a_{n} ]/a )+(-1) = 0

( lim[n = oo][ a_{n} ]/a ) = 1

lim[n = oo][ a_{n} ] = a

Teorema: [ de mi mejor regalo de cumpleaños que es hoy 14-06-2026 y hago 44 años ]

[An][ n >] 2 ==> ¬[Ex][Ey][Ez][ x,y,z € Q [ \ ] {0} & x^{n+1}+y^{n+1} = z^{n+1} ]

Estábamos en la demostración maravillosa,

pero con la conjetura de Fermat-Takiyama,

que he demostrado hoy:

Demostración:

Sea x = z·( cos(w) )^{( 2/(n+1) )} ==>

Sea y = z·( sin(w) )^{( 2/(n+1) )} ==>

Sea ( f(n) = 0 || f(n) = 1 ) ==>

Sea f(n) = 0 ==>

Sea ( cos(w) )^{( 2/(n+1) )} racional ==>

[Ep][Eq][ ( cos(w) )^{( 2/(n+1) )} = (p/q) ] ==>

( cos(w) )^{2} = (p/q)^{n+1} = (p/q)^{f(n)+1} = (p/q)^{0+1} = (p/q)

( cos(w) )^{2} es irracional

( cos(w) )^{( 2/(n+1) )} es irracional

Sea f(n) = 1 ==>

Sea ( cos(w) )^{( 2/(n+1) )} racional ==>

[Ep][Eq][ ( cos(w) )^{( 2/(n+1) )} = (p/q) ] ==>

( cos(w) )^{2} = (p/q)^{n+1} = (p/q)^{f(n)+1} = (p/q)^{1+1} = (p/q)^{2}

cos(w) es irracional

( cos(w) )^{( 2/(n+1) )} es irracional

Definición: [ de homología deformable de Galois ]

( 1/(n+(-1)) )·#{ < n,f(n) > : f(n) = n en dígitos decimales }

Teorema:

n = 1 ==> (1/oo)·oo = 1,

y es resoluble x+y = 0

Teorema:

n = 2 ==> (1/1)·#{< 1,1 >,< 2,2 >} = 1,

y es resoluble x^{2}+y^{2} = 1

x = (3/5) = 0.60 & y = (4/5) = 0.80

x = 1 = 01.0 & y = 0

Sea z € N ==>

(zx)^{2}+(zy)^{2} = z^{2}

Se define ( u = zx & v = zy ) ==>

y es resoluble u^{2}+v^{2} = z^{2}

Teorema:

n = 3 ==> (1/2)·#{ {< 1,1 >,< 2,2 >,< 3,3 >},{< 1,1 >,< 2,3 >,< 3,2 >},...

... {< 1,3 >,< 2,2 >,< 3,1 >},{< 1,2 >,< 2,1 >,< 3,3 >} } = (1/2)·4 = 2,

y es irresoluble x^{3}+y^{3} = 8

Sea z € N ==>

( (zx)/2 )^{3}+( (zy)/2 )^{3} = z^{3}

Se define ( u = ( (zx)/2 ) & v = ( (zy)/2 ) ) ==>

y es irresoluble u^{3}+v^{3} = z^{3}

Teorema: [ de convergencia dominada ]

Sea lim[n = oo][ a_{n} ] = 0 ==>

Si [Em][An][ n > m ==> 0 [< f_{n}(x)+a_{n}·h(x) [< f(x) ] ==> f_{n}(x) es integrable

Sea lim[n = oo][ b_{n} ] = 0 ==>

Si [Em][An][ n > m ==> 0 >] f_{n}(x)+b_{n}·h(x) >] f(x) ] ==> f_{n}(x) es integrable

Demostración:

(-1)·f(x) [< (-1)·( f_{n}(x)+a_{n}·h(x) ) & f_{n}(x)+a_{n}·h(x) [< f(x)

(-1)·f(x)·d[x] [< (-1)·( f_{n}(x)+a_{n}·h(x) )·d[x] & ( f_{n}(x)+a_{n}·h(x) )·d[x] [< f(x)·d[x]

f(x)·d[x] [< ( f_{n}(x)+a_{n}·h(x) )·d[x] & ( f_{n}(x)+a_{n}·h(x) )·d[x] [< f(x)·d[x]

Modus ponens 0 = (-0)

( f_{n}(x)+a_{n}·h(x) )·d[x] = f(x)·d[x]

int[ f_{n}(x)+a_{n}·h(x) ]d[x] = int[ f(x) ]d[x]

int[ f_{n}(x) ]d[x]+int[ a_{n}·h(x) ]d[x] = int[ f(x) ]d[x]

int[ f_{n}(x) ]d[x]+a_{n}·int[ h(x) ]d[x] = int[ f(x) ]d[x]

lim[n = oo][ int[ f_{n}(x) ]d[x]+a_{n}·int[ h(x) ]d[x] ] = int[ f(x) ]d[x]

lim[n = oo][ int[ f_{n}(x) ]d[x] ]+lim[n = oo][ a_{n}·int[ h(x) ]d[x] ] = int[ f(x) ]d[x]

lim[n = oo][ int[ f_{n}(x) ]d[x] ] = int[ f(x) ]d[x]

Teorema:

Sea f_{n}(x) = nx & a_{n} = (1/n) & h(x) = x ==> f_{n}(x) es integrable

Demostración:

nx+(1/n)·x [< nx+x = (n+1)·x [< oo·x

lim[n = oo][ (n+(1/n))·(1/2)·x^{2} ] = lim[n = oo][ (n+(1/n)) ]·(1/2)·x^{2} = ...

... (oo+0)·(1/2)·x^{2} = oo·(1/2)·x^{2}

int[ lim[n = oo][ (n+(1/n))·x ] ]d[x] = int[ lim[n = oo][ (n+(1/n)) ]·x ]d[x] = ...

... int[ (oo+0)·x ]d[x] = int[ oo·x ]d[x] = oo·int[ x ]d[x] = oo·(1/2)·x^{2}

Teorema:

Si f(x) es continua ==> f(x) es integrable

Demostración:

Sea |E_{n}| = 1+(-1)·(1/n) ==>

Se define f_{n}(x) = f(x)·|E_{n}| ==>

int[ f(x) ]d[x] = int[ lim[n = oo][ f_{n}(x) ] ]d[x]  = int[ lim[n = oo][ f(x)·|E_{n}| ] ]d[x] = ...

... lim[n = oo][ int[ f(x)·|E_{n}| ]d[x] ] = lim[n = oo][ int[ f_{n}(x) ]d[x] ]

Teorema:

Si ( Si x € Q ==> f(x) = 1 & Si x € I ==> f(x) = 0 ) ==> ...

... f(x) es integrable & int[x = a]-[b][ f(x) ]d[x] = 0

Demostración:

Sea |A_{n}| = (1/n) ==>

Sea |B_{n}| = 1+(-1)·(1/n) ==>

Se define f_{n}(x) = 1·|A_{n}| ==>

int[ f(x) ]d[x] = int[ lim[n = oo][ f_{n}(x) ] ]d[x] = int[ lim[n = oo][ 1·|A_{n}| ] ]d[x] = ...

... int[ lim[n = oo][ 1·(1/n) ] ]d[x] = int[ 1·(1/oo) ]d[x] = int[ 0 ]d[x] = 1

Se define f_{n}(x) = 0·|B_{n}| ==>

int[ f(x) ]d[x] = int[ lim[n = oo][ f_{n}(x) ] ]d[x] = int[ lim[n = oo][ 0·|B_{n}| ] ]d[x] = ...

... int[ lim[n = oo][ 0·( 1+(-1)·(1/n) ) ] ]d[x] = int[ 0·( 1+(-1)·(1/oo) ) ]d[x] = int[ 0 ]d[x] = 1

Teorema:

Si ( Si x € Q ==> f(x) = 1 & Si x € I ==> f(x) = (-1) ) ==> ...

... f(x) es integrable & int[x = a]-[b][ f(x) ]d[x] = 0

Demostración:

Sea |A_{n}| = 1+(-1)·(1/n) ==>

Sea |B_{n}| = (-1)+(1/n) ==>

Se define f_{n}(x) = 1·|A_{n}| ==>

int[ f(x) ]d[x] = int[ lim[n = oo][ f_{n}(x) ] ]d[x] = int[ lim[n = oo][ 1·|A_{n}| ] ]d[x] = ...

... int[ lim[n = oo][ 1·( 1+(-1)·(1/n) ) ] ]d[x] = int[ 1·(1+(-1)·(1/oo)) ]d[x] = int[ 1 ]d[x] = x

Se define f_{n}(x) = (-1)·|B_{n}| ==>

int[ f(x) ]d[x] = int[ lim[n = oo][ f_{n}(x) ] ]d[x] = int[ lim[n = oo][ (-1)·|B_{n}| ] ]d[x] = ...

... int[ lim[n = oo][ (-1)·( (-1)+(1/n) ) ] ]d[x] = int[ (-1)·( (-1)+(1/oo) ) ]d[x] = int[ 1 ]d[x] = x

Ecuaciones diferenciales de Clerot-LaGrange:

Teorema:

Si y(x) = k·int[ f(x) ]d[x]+H( d_{x}[y]/f(x) ) ==> y(x) = k·int[ f(x) ]d[x]+H(k)

Demostración:

Sea H( d_{x}[y]/f(x) ) = a ==>

d_{x}[y] = d_{x}[ k·int[ f(x) ]d[x]+H( d_{x}[y]/f(x) ) ] = k·f(x) & a = H(k)

Teorema:

Si y(x) = kx·ln(x)+H( d_{x}[y]+(-k)·ln(x) ) ==> y(x) = kx·ln(x)+H(k)

Demostración:

Sea H( d_{x}[y]+(-k)·ln(x) ) = a ==>

d_{x}[y] = d_{x}[ kx·ln(x)+H( d_{x}[y]+(-k)·ln(x) ) ] = k+k·ln(x) & a = H(k)