d_{rw}[f(w,x)]+d_{x}[f(w,x)] = a·( sin(2arw)+(-1)·(1/(ax))^{n} )
f(w,x) = ( sin(arw) )^{2}+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )
d_{rw}[g(w,x)]+d_{x}[g(w,x)] = a·( (-1)·sin(2arw)+(1/(ax))^{n} )
g(w,x) = ( cos(arw) )^{2}+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )
( f(w,x)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) )·...
... ( g(w,x)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ) = (1/4) <==> ...
... w = (1/(ar))·(pi/4)
( f(w,x)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) )·...
... ( g(w,x)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ) = (3/16) <==> ...
... ( w = (1/(ar))·(pi/3) || w = (1/(ar))·(pi/6) )
Deducción:
( sin(arw) )^{2}·( cos(arw) )^{2} = (1/4)
( cos(arw) )^{2} = 1+(-1)·( sin(arw) )^{2}
( sin(arw) )^{4}+(-1)·( sin(arw) )^{2}+(1/4) = 0
( sin(arw) )^{2} = (1/2)·( 1+( 1+(-1) )^{(1/2)}) = (1/2)
arw = arc-sin( (1/2)^{(1/2)} ) = (pi/4)
Ley:
d_{rw}[f(w,x)]+d_{x}[f(w,x)] = a·( ( sin(arw) )^{2}+(-1)·(1/(ax))^{n} )
f(w,x) = (1/2)·arw+(-1)·(1/4)·sin(2arw) )+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )
d_{rw}[g(w,x)]+d_{x}[g(w,x)] = a·( ( cos(arw) )^{2}+(1/(ax))^{n} )
g(w,x) = (1/2)·arw+(1/4)·sin(2arw) )+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )
int[ f(w,x)+g(w,x) ]d[arw] = 2pi^{2} <==> w = (1/(ar))·2pi
Deducción:
int[ arw ]d[arw] = (1/2)·(arw)^{2} = 2pi^{2}
(arw)^{2} = 4pi^{2} = (2pi)^{2}
Principio: [ de la primera directriz ]
Hay contacto extraterrestre,
con motor de curvatura,
siendo el próximo,
pudiendo ir a su planeta.
No hay contacto extraterrestre,
sin motor de curvatura,
siendo el prójimo,
no pudiendo ir a su planeta.
Ley:
No puede haber contacto extraterrestre,
saltando-te la primera directriz,
porque te crees un dios del universo.
Puede haber contacto extraterrestre,
no saltando-te la primera directriz,
porque no te crees un dios del universo.
Ley:
Pensamiento peligroso:
Te crees un dios del universo
y entonces también te crees que caminas solo sin estar allí.
Pensamiento seguro:
Quizás te cree un dios del universo
pero no te crees que caminas solo sin estar allí.
Principio: [ de la segunda directriz ]
No puede haber contacto extraterrestre des-ascendido,
con un mundo ascendido,
porque no se puede estar en un mundo des-ascendido,
con testimonio del evangelio,
siendo el prójimo de ti el mundo des-ascendido.
Puede haber contacto extraterrestre des-ascendido,
con un mundo des-ascendido,
porque se puede estar en un mundo des-ascendido,
sin testimonio del evangelio,
siendo el próximo de ti el mundo des-ascendido.
Ley:
Todos los hombres que se creen dioses del universo,
son de la Tierra,
y no de Cygnus-Kepler,
porque se han saltado la segunda directriz.
Todos los hombres que no se creen dioses del universo,
son de Cygnus-Kepler,
y no de la Tierra,
porque no se han saltado la segunda directriz.
Análisis matemático 2:
Arte:
Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>
[Es][ sum[n = 1]-[oo][ (s+(-1))·(1/n)^{s} ] = ( Z(s)/Z(s+(-1)) ) ]
Exposición:
s = 1
( Z(s)/Z(s+(-1)) ) = ln(2)
f(s+(-1)) = ( 1/(s+(-1)) )
Id(s+(-1)) = ( 1/(s+(-1)) ) <==> s = 2
g( h(s+(-1)) ) = Z(s+(-1))
Id( h(s+(-1)) ) = Z(s+(-1)) <==> h = Z
sum[n = 1]-[oo][ (s+(-1))·(1/n)^{s} ] = (s+(-1))·sum[n = 1]-[oo][ (1/n)^{s} ] = ...
.... (s+(-1))·Z(s) = f(s+(-1))·Z(s) = ( 1/(s+(-1)) )·Z(s) = ...
... ( 1/(g o h)(s+(-1)) ) )·Z(s) = ( 1/g( h(s+(-1)) ) )·Z(s) = ( Z(s)/Z(s+(-1)) )
Arte:
Sea H(s) = sum[n = 1]-[oo][ (1+(1/n))^{s} ] ==>
[Es][ sum[n = 1]-[oo][ 0s·(1+(1/n))^{s} ] = ( H(s)/H(s+(-1)) ) ]
Exposición:
s = 1
( H(s)/H(s+(-1)) ) = 1+ln(2)
Arte:
Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>
[Es][ sum[n = 1]-[oo][ 0·[ n // s ]·(1/n)^{s} ] = (s+(-1))·Z(s+(-1)) ]
Exposición:
s = 1
u(s) = 1
v(1) = s
sum[n = 1]-[oo][ 0·[ n // s ]·(1/n)^{s} ] = sum[n = 1]-[oo][ 0·[ n // u(s) ]·(1/n)^{u(s)} ] = ...
... sum[n = 1]-[oo][ 0·[ n // 1 ]·(1/n) ] = sum[n = 1]-[oo][ 0n·(1/n) ] = sum[n = 1]-[oo][ 0 ] = 1 = ...
... 0·oo = 0·Z(0) = (1+(-1))·Z(1+(-1)) = (v(1)+(-1))·Z(v(1)+(-1)) = (s+(-1))·Z(s+(-1))
Arte:
Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>
[Es][ sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // s ]·(1/n)^{s} ] = 2s·(s+(-1))·Z(s+(-1)) ]
Exposición:
s = 1
u(s) = 1
v(1) = s
sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // s ]·(1/n)^{s} ] = ...
... sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // u(s) ]·(1/n)^{u(s)} ] = ...
... sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // 1 ]·(1/n) ] = sum[n = 1]-[oo][ (1/2)^{n+(-1)}·n·(1/n) ] = ...
... sum[n = 1]-[oo][ (1/2)^{n+(-1)} ] = 2 = 2·0·oo = 2·0·Z(0) = (1+1)·(1+(-1))·Z(1+(-1)) = ...
... (v(1)+v(1))·(v(1)+(-1))·Z(v(1)+(-1)) = (s+s)·(s+(-1))·Z(s+(-1)) = 2s·(s+(-1))·Z(s+(-1))
Análisis matemático 1:
[%] Derivación
Continuidad
Cuerpos ordenados
Sucesiones
Análisis matemático 2:
[%] Integración y producto integral
Integral definida
Euler Falsus Infinitorum
Teoremas y Artes de series
Análisis matemático 3:
[%] Derivadas parciales
[%] Optimización
Continuidad
Análisis matemático 4:
[%] Integrales múltiples
[%] Integrales de línea
Integrales impropias
Análisis matemático 5:
Sucesiones de funciones
Integral de Lebesgue
Series de potencies
Análisis matemático 6:
Transformada integral exponencial
Arte método de Euler
Arte series de Laurent
Teorema:
Sea d_{x}[F(x)] = f(x) ==>
F(x) es continua <==> f(x) es continua
Demostración:
Sea s > 0 ==>
Sea d < (s/2) ==>
| F(x+h)+(-1)·F(x) | < d
| F(x+h)+(-1)·F(x) | = 0
| f(x+h)+(-1)·f(x) | = 0^{2} = 2·0 < 2d < s
Sea d > 0 ==>
Sea s > 0 ==>
| f(x+h)+(-1)·f(x) | < s < 2s
| f(x+h)+(-1)·f(x) | = 2·0 = 0^{2}
| F(x+h)+(-1)·F(x) | = 0
| F(x+h)+(-1)·F(x) | < d
Análisis matemático 2:
Teorema:
lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{0}·(b+(-a))·(1/n) ] ] = b+(-a)
Demostración:
lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{0}·(b+(-a))·(1/n) ] ] = ...
... lim[n = oo][ sum[k = 1]-[n][ (b+(-a))·(1/n) ] ] = lim[n = oo][ (b+(-a))·(n/n) ] = b+(-a)
Teorema:
lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )·(b+(-a))·(1/n) ] ] = (1/2)·b^{2}+(-1)·(1/2)·a^{2}
Demostración:
lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )·(b+(-a))·(1/n) ] ] = ...
... lim[n = oo][ a·(b+(-a))·(n/n)+(1/2)·n·(n+1)·(b+(-a))^{2}·(1/n)^{2} ] = ...
... ab+(-1)·a^{2}+(1/2)·b^{2}+(-1)·ab+(1/2)·a^{2} = (1/2)·b^{2}+(-1)·(1/2)·a^{2}
Teorema:
lim[n = oo][ sum[k = 1]-[n][ e^{a+(k/n)·(b+(-a))}·(b+(-a))·(1/n) ] ] = e^{b}+(-1)·e^{a}
Demostración:
lim[n = oo][ sum[k = 1]-[n][ e^{a+(k/n)·(b+(-a))}·(b+(-a))·(1/n) ] ] = ...
... lim[n = oo][ e^{a}·( ( e^{((1/n)+1)·(b+(-a))}+(-1) )/( e^{(1/n)·(b+(-a))}+(-1) ) )·(b+(-a))·(1/n) ] = ...
... e^{b}+(-1)·e^{a}
Teorema:
lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{2}·(b+(-a))·(1/n) ] ] = (1/3)·b^{3}+(-1)·(1/3)·a^{3}
Demostración:
lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{2}·(b+(-a))·(1/n) ] ] = ...
... lim[n = oo][ ( a^{2}·(n/n)+2·(1/2)·n·(n+1)·a·(b+(-a))·(1/n)^{2}+...
... (1/6)·n·(n+1)·(2n+1)·(b+(-a))^{2}·(1/n)^{3} )·(b+(-a)) ] = ...
... ab·(b+(-a))+(1/3)·b^{3}+(-1)·ab·(b+(-a))+(-1)·(1/3)·a^{3} = (1/3)·b^{3}+(-1)·(1/3)·a^{3}
Teorema:
lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{3}·(b+(-a))·(1/n) ] ] = (1/4)·b^{4}+(-1)·(1/4)·a^{4}
Demostración:
lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{3}·(b+(-a))·(1/n) ] ] = ...
... lim[n = oo][ ( a^{3}·(n/n)+(3/2)·n·(n+1)·a^{2}·(b+(-a))·(1/n)^{2}+...
... (1/2)·n·(n+1)·(2n+1)·a·(b+(-a))^{2}·(1/n)^{3}+...
... (1/4)·n^{2}·(n^{2}+2n+1)·(b+(-a))^{3}·(1/n)^{4} )·(b+(-a)) ] = (1/4)·b^{4}+(-1)·(1/4)·a^{4}
(-1)·a^{4}+(3/2)·a^{4}+(-1)·a^{4}+(1/4)·a^{4} = (-1)·(1/4)·a^{4}
(3/2)·(ab)^{2}+(-3)·(ab)^{2}+(3/2)·(ab)^{2} = 0
a^{3}b+(-3)·a^{3}b+3a^{3}b+(-1)·a^{3}b = 0
ab^{3}+(-1)·ab^{3} = 0
Teorema:
lim[n = oo][ sum[k = 1]-[n][ (k/n)·(1/n) ] ] = (1/2)
Demostración:
lim[n = oo][ sum[k = 1]-[n][ (k/n)·(1/n) ] ] = ...
... lim[n = oo][ (1/2)·n·(n+1)·(1/n)^{2} ] = (1/2) = (1/2)·1^{2}+(-1)·(1/2)·0^{2}
Teorema:
lim[n = oo][ sum[k = 1]-[n][ e^{(k/n)}·(1/n) ] ] = e+(-1)
Demostración:
lim[n = oo][ sum[k = 1]-[n][ e^{(k/n)}·(1/n) ] ] = ...
... lim[n = oo][ ( (e^{(1/n)+1}+(-1))/(e^{(1/n)}+(-1)) )·(1/n) ] = e+(-1) = e^{1}+(-1)·e^{0}
Definición:
lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = int[x = 0]-[1][ f(x) ]d[x]
Teorema:
lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = F(1)+(-1)·F(0)
Demostración:
lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = int[x = 0]-[1][ f(x) ]d[x] = F(1)+(-1)·F(0)
Teorema:
lim[n = oo][ sum[k = 1]-[n][ (p+1)·k^{p}·f( (k/n)^{p+1} )·(1/n)^{p+1} ] ] = F(1)+(-1)·F(0)
Demostración:
lim[n = oo][ sum[k = 1]-[n][ (p+1)·k^{p}·f( (k/n)^{p+1} )·(1/n)^{p+1} ] ] = ...
... lim[n = oo][ sum[k = 1]-[n][ (p+1)·(k/n)^{p}·f( (k/n)^{p+1} )·(1/n) ] ] = ...
... int[x = 0]-[1][ (p+1)·x^{p}·f(x^{p+1}) ]d[x] = [ F(x^{p+1}) ]_{x = 0}^{x = 1} = ...
... F(1)+(-1)·F(0)
Teorema:
lim[n = oo][ sum[k = 1]-[n][ ( 1/(n^{p}+k^{p}) )·pk^{p+(-1)} ] ] = ln(2)
Teorema:
lim[n = oo][ sum[k = 1]-[n][ (npk^{p+(-1)}+k^{p})·e^{(k/n)}·(1/n)^{p+1} ] ] = e
Teorema:
int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = p!·( e+(-1) )
Demostración:
int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] e^{x}
Teorema:
int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = p!·( 1+(-1)·(1/e) )
Demostración:
int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] (-1)·e^{(-x)}
Teorema:
int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = p!·( e+(-1) )
Demostración: [ por inducción ]
int[x = 0]-[1][ x^{p+1}·e^{x} ]d[x] = ...
... [ x^{p+1}·e^{x} ]_{x = 1}^{x = 1}+(-1)·(p+1)·int[x = 1]-[0][ x^{p}·e^{x} ]d[x] = ...
... [ x^{p+1}·e^{x} ]_{x = 1}^{x = 1}+(p+1)·int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = ...
... (-1)·(p+1)·p!·int[x = 1]-[0][ e^{x} ]d[x] = (-1)·(p+1)!·int[x = 1]-[0][ e^{x} ]d[x] = (p+1)!·( e+(-1) )
Teorema:
int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = p!·( 1+(-1)·(1/e) )
Demostración: [ por inducción ]
int[x = 0]-[1][ x^{p+1}·e^{(-x)} ]d[x] = ...
... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(p+1)·int[x = 1]-[0][ x^{p}·e^{(-x)} ]d[x] = ...
... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(-1)·(p+1)·int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = ...
... (-1)·(p+1)·p!·int[x = 1]-[0][ e^{(-x)} ]d[x] = ...
... (-1)·(p+1)!·int[x = 1]-[0][ e^{(-x)} ]d[x] = (p+1)!·( 1+(-1)·(1/e) )
Teorema:
int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = p!
Demostración:
int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] e^{x}
Teorema:
int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = p!
Demostración:
int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] (-1)·e^{(-x)}
Teorema:
int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = p!
Demostración: [ por inducción ]
int[x = (-oo)]-[0][ x^{p+1}·e^{x} ]d[x] = ...
... [ x^{p+1}·e^{x} ]_{x = 0}^{x = 0}+(-1)·(p+1)·int[x = 0]-[(-oo)][ x^{p}·e^{x} ]d[x] = ...
... [ x^{p+1}·e^{x} ]_{x = 0}^{x = 0}+(p+1)·int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = ...
... (-1)·(p+1)·p!·int[x = 0]-[(-oo)][ e^{x} ]d[x] = (-1)·(p+1)!·int[x = 0]-[(-oo)][ e^{x} ]d[x] = (p+1)!
Teorema:
int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = p!
Demostración: [ por inducción ]
int[x = 0]-[oo][ x^{p+1}·e^{(-x)} ]d[x] = ...
... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(p+1)·int[x = oo]-[0][ x^{p}·e^{(-x)} ]d[x] = ...
... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(-1)·(p+1)·int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = ...
... (-1)·(p+1)·p!·int[x = oo]-[0][ e^{(-x)} ]d[x] = (-1)·(p+1)!·int[x = oo]-[0][ e^{(-x)} ]d[x] = (p+1)!
Teorema: [ de Hôpital-Garriga ]
Si f(x) = 1 ==> f(x) = d_{x}[f(x)] en una indeterminación
Demostración:
d_{x}[f(x)] = (1/h)·( f(x+h)+(-1)·f(x) ) = (1/h)·( 1+(-1) ) = (0/0) = 1 = f(x)
Teorema: [ de Hôpital-Garriga ]
Si f(x) = (-1) ==> f(x) = d_{x}[f(x)] en una indeterminación
Demostración:
d_{x}[f(x)] = (1/h)·( f(x+h)+(-1)·f(x) ) = (1/h)·( 1+(-1) ) = ((-0)/0) = (-1) = f(x)
Teorema: [ de Hôpital-Garriga ]
Si f(x) = 0^{n} ==> f(x) = d_{x}[f(x)] en una indeterminación
Demostración:
d_{x}[f(x)] = (1/h)·( f(x+h)+(-1)·f(x) ) = (1/h)·( 0^{n}+(-1)·0^{n} ) = (1/0)·0^{n+1} = 0^{n} = f(x)
Teorema: [ de Hôpital-Garriga ]
Si f(x) = oo^{n} ==> f(x) = d_{x}[f(x)] en una indeterminación
Demostración:
d_{x}[f(x)] = (1/h)·( f(x+h)+(-1)·f(x) ) = (1/h)·( oo^{n}+(-1)·oo^{n} ) = ...
... (1/0)·oo^{n+(-1)} = oo^{n} = f(x)
Ley: [ de ejemplo de teoría ]
Si d_{V}[P_{0}]·V^{2}+PV+(-1)·d_{P}[k]·TP = 0 ==>
V_{min} = (-1)·(1/2)·( 1/d_{V}[P_{0}] )·P
(1/4)·( 1/d_{V}[P_{0}] )·P^{2}+d_{P}[k]·TP = 0
P_{min} = (-1)·2·d_{P}[k]·T·d_{V}[P_{0}]
(PV)_{min} = d_{P}[k]·TP
d_{P}[T(P)]·p = qR <==> p = qR·( 1/(PV)_{min} )·d_{P}[k]·(-1)·P^{2}
Deducción:
d_{V}[ d_{V}[P_{0}]·V^{2}+PV+(-1)·d_{P}[k]·TP ] = ...
... d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV]+d_{V}[ (-1)·d_{P}[k]·TP ] = ...
... d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV]+0 = d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV] = ...
... d_{V}[P_{0}]·d_{V}[V^{2}]+P·d_{V}[V] = d_{V}[P_{0}]·2V+P
d_{V}[P_{0}]·2V+P = 0
d_{V}[P_{0}]·2V = d_{V}[P_{0}]·2V+0 = d_{V}[P_{0}]·2V+(P+(-P)) = ...
... ( d_{V}[P_{0}]·2V+P )+(-P) = 0+(-P) = (-P)·
V = ( (1/2)·(1/d_{V}[P_{0}])·(d_{V}[P_{0}]·2) )·V = ...
... (1/2)·(1/d_{V}[P_{0}])·( (d_{V}[P_{0}]·2)·V ) = (-1)·(1/2)·(1/d_{V}[P_{0}])·P
d_{P}[T(P)] = (PV)_{min}·(1/d_{P}[k])·(-1)·(1/P)^{2}
Ley:
Si ( P+d_{xyz}^{3}[q(x,y,z)]·gh )·V = kT ==>
q(x,y,z) = kT·(1/(gh))·(1/V)·xyz+(-1)·P·(1/(gh))·xyz
Ley:
Si ( P+d_{xy}^{2}[q(x,y)]·g )·V = kT ==>
q(x,y) = kT·(1/g)·(1/V)·xy+(-1)·P·(1/g)·xy
Ley:
Si ( P+d_{xy}^{2}[q(x,y)]·g )·V = kT·xya^{2} ==>
q(x,y) = kT·(1/g)·(1/V)·(1/4)·(axy)^{2}+(-1)·P·(1/g)·xy
Ley:
Si ( P+d_{x}[m(x)]·u^{2} )·V = kT ==>
m(x) = kT·(1/u)^{2}·(1/V)·x+(-1)·P·(1/u)^{2}·x
Rezo al Mal:
Los hombres no tienen motor de curvatura,
y no pueden ir a ver a su mujer,
pero no son maricones.
Los extraterrestres tienen motor de curvatura,
y pueden ir a ver a su mujer,
pero son maricones.
Definición:
er-h[p](x) = sum[k = 0]-[oo][ (1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ]
er-h[p](x) = sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·x^{k} ] = ...
... (1/(p+1))·x^{p+1} [o(x)o] e^{x}
er-h[p](-x) = sum[k = 0]-[oo][ (-1)^{k}·(1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ]
er-h[p](-x) = sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (-1)^{k}·(1/k!)·x^{k} ] = ...
... sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·(-x)^{k} ] = (1/(p+1))·x^{p+1} [o(x)o] e^{(-x)}
Teorema:
int[ x^{p}·e^{x} ]d[x] = er-h[p](x)
int[ x^{p}·e^{(-x)} ]d[x] = (-1)·er-h[p](-x)
Teorema:
er-h[p](1) = p!·e
er-h[p](0) = p!
er-h[p](-1) = p!·(1/e)
Demostración:
er-h[p](x) = sum[j = 0]-[oo][ (1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ] = ...
... sum[j = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·x^{k} ] = p!·sum[j = 0]-[oo][ (1/k!)·x^{k} ]
Teorema:
d_{x}[er-h[p](-x)] = (-1)·x^{p}·e^{(-x)}
Demostración:
j = k+(-1)
d_{x}[er-h[p](-x)] = sum[k = 0]-[oo][ (-1)^{k}·(1/(k+(-1))!)·x^{(k+(-1))+p} ] = ...
... sum[k = 0]-[oo][ (-1)^{j+1}·(1/j!)·x^{j+p} ] = ...
... (-1)·x^{p}·sum[k = 0]-[oo][ (-1)^{j}·(1/j!)·x^{j} ] = ...
... (-1)·x^{p}·sum[k = 0]-[oo][ (1/j!)·(-x)^{j} ] = (-1)·x^{p}·e^{x}
Principio:
El que es,
es.
El que no es,
no es.
Ley:
Afirmación Verdadera:
El fiel es,
y el infiel no es.
Negación Falsa:
El fiel no es,
y el infiel es.
Ley:
Afirmación Verdadera:
No es ninguien,
no siendo los infieles,
estando todo fiel muerto.
Negación Falsa:
Es toto-hoimbre,
siendo los fieles,
estando todo-algún fiel vivo.
Anexo
Esta falsedad no es de Cygnus-Kepler,
porque hay fieles ascendidos,
y no lo puede decir el Mal.
Rezo al Mal desde Cygnus-Kepler:
Yo que soy hombre,
no soy,
amando al próximo,
no como a mi mismo.
Él que es extraterrestre,
es,
amando al prójimo,
como a mi mismo.
Teorema:
p^{m} =[m]= p
Demostración: [ por inducción ]
(p+1)^{m} = p^{m}+mk+1 =[m]= p^{m}+1 =[m]= p+1
Teorema:
p^{m} =[m]= mp
Demostración: [ por inducción ]
(p+1)^{m} = p^{m}+mk+1 =[m]= p^{m}+1 =[m]= mp+1
Definición:
f(a) = b <==> a =[m]= b
Teorema:
f(1) = 1
Demostración:
1 =[m]= 1
Teorema:
f(a+b) = f(a)+f(b)
Demostración:
a+b =[m]= a+b
f(a+b) = a+b
a =[m]= a & b =[m]= b
f(a+b) = a+b = f(a)+f(b)
Teorema:
f(ab) = f(a)·f(b)
Demostración:
ab =[m]= ab
f(ab) = ab
a =[m]= a & b =[m]= b
f(ab) = ab = f(a)·f(b)
Teorema:
Si a =[m]= 1 ==> sum[r = 0]-[m+(-1)][ f(a) ] = m+(-1)
Demostración:
a =[m]= 1
f(a) = 1
Teorema:
Si a =[m]= p^{m+(-1)} ==> sum[r = 0]-[m+(-1)][ f(a) ] = m+(-1)
Demostración:
a =[m]= p^{m+(-1)} =[m]= 1
f(a) = 1
Teorema:
Si a =[2]= 0 ==>
x^{2}+ax =[2]= p <==> x =[2]= p
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)+f(ax) = f(x+ax) = p
x =[2]= p
Teorema:
Si a =[2]= 1 ==>
x^{2}+ax =[2]= p <==> x =[2]= p
Demostración:
a =[2]= 1
f(a) = 1
ax =[2]= 2x+ax =[2]= x^{2}+ax =[2]= p
f(x) = f(a)·f(x) = f(ax) = p
x =[2]= p
Definición: [ de función de Euler ]
H(ab) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·b·Prod[q | b][ (2+(-1)·(1/q)) ]
Teorema:
H(1) = 1
Demostración:
H(1) = H(1·1) = 1·Prod[p | 1][ ( 2+(-1)·(1/p) ) ]·1·Prod[q | 1][ (2+(-1)·(1/q)) ] = 1
Teorema:
H(a) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]
Demostración:
H(a) = H(a·1) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·1·Prod[q | 1][ (2+(-1)·(1/q)) ] = ...
... a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·1
Teorema:
H(ab) = H(a)·H(b)
Demostración:
H(a·b) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·b·Prod[q | b][ (2+(-1)·(1/q)) ] = H(a)·H(b)
Teorema:
H(p^{m}) = 2p^{m}+(-1)·p^{m+(-1)}
Teorema:
H(p) = 2p+(-1)
Teorema:
Sea p =[m]= n ==>
p^{m} =[m]= 2n+(-1) <==> p =[m]= n =[m]= 1
Demostración:
p^{m}·(2p+(-1)) =[m]= (2n+(-1))·(2p+(-1))
H(p^{m+1}) =[m]= H(n)·H(p) = H(np)
p^{m+1} =[m]= np
p^{m} =[m]= n
2n+(-1) =[m]= p^{m} =[m]= n
n =[m]= 1
p =[m]= n =[m]= 1
Teorema:
3^{2} =[2]= 5 <==> 3 =[2]= 1
Demostración:
9+(-5) = 4 = 2·2
3+(-1) = 2
Teorema:
4^{3} =[3]= 7 <==> 4 =[3]= 1
Demostración:
64+(-7) = 57 = 3·19
4+(-1) = 3
Teorema:
5^{4} =[4]= 9 <==> 5 =[4]= 1
Demostración:
625+(-9) = 616 = 4·154
5+(-1) = 4
Teorema:
8^{7} =[7]= 15 <==> 8 =[7]= 1
Demostración:
2,097,152+(-15) = 2,097,137 = 7·299,591
8+(-1) = 7
Teorema:
9^{8} =[8]= 17 <==> 9 =[8]= 1
Demostración:
43,046,721+(-17) = 43,046,704 = 8·5,380,838
9+(-1) = 8
Teorema:
x^{2} =[2]= a <==> x =[2]= a
Demostración:
Sea x = y+a ==>
(y+a)^{2} = y^{2}+2ya+a^{2} =[2]= y+a
y+a =[2]= a
x+(-a) = y =[2]= 0
Teorema:
x^{2} =[2]= 2k <==> x =[2]= 2k
Demostración:
4k^{2}+(-2)·k = 2·( 2k^{2}+(-k) )
Teorema:
x^{2} =[2]= 2k+1 <==> x =[2]= 2k+1
Demostración:
4k^{2}+4k+1+(-2)·k+(-1) = 2·( 2k^{2}+k )
Teorema:
x^{3} =[3]= a <==> x =[3]= a
Demostración:
Sea x = y+a ==>
(y+a)^{3} = y^{3}+3y^{2}a+3ya^{2}+a^{3} =[3]= y+a
y+a =[3]= a
x+(-a) = y =[3]= 0
Teorema:
x^{3} =[3]= 3k <==> x =[3]= 3k
Demostración:
27k^{3}+(-3)·k = 3·( 9k^{3}+(-k) )
Teorema:
x^{3} =[3]= 3k+1 <==> x =[3]= 3k+1
Demostración:
27k^{3}+27k^{2}+9k+1+(-3)·k+(-1) = 3·( 9k^{3}+9k^{2}+2k )
Teorema:
x^{3} =[3]= 3k+2 <==> x =[3]= 3k+2
Demostración:
27k^{3}+54k^{2}+36k+8+(-3)·k+(-2) = 3·( 9k^{3}+18k^{2}+11k+2 )
Teorema:
a^{2} =[4]= 2a
Demostración:
a = 2k
Teorema:
a =[4]= 1
Demostración:
a = 4k+1
Teorema:
x^{4} =[4]= a <==> ( 2x =[4]= a || 2x+1 =[4]= 3a )
Demostración:
Sea x = y+a ==>
(y+a)^{4} = y^{4}+4y^{3}a+6·(ya)^{2}+4ya^{3}+a^{4} =[4]= ( y^{2}+a^{2} )^{2} =[4]= ...
... 2y^{2}+2a^{2} =[4]= 2y+2a
2y+2a =[4]= a
2x+(-a) = 2y+a =[4]= 0
2y^{2}+2a^{2} =[4]= 2y+1 =[4]= a
2x+1 =[4]= 3a
Teorema:
x^{4} =[4]= 4k <==> x =[4]= 2k
Demostración:
16k^{4}+(-4)·k = 4·( 4k^{4}+(-k) )
Teorema:
x^{4} =[4]= 4k+1 <==> x =[4]= 2k+1 =[4]= 6k+1
Demostración:
1,296k^{4}+864k^{3}+216k^{2}+24k+1+(-4)·k+-1 = 4·( 324k^{4}+216k^{2}+54k^{2}+5k )
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