Ley:
d_{tt}^{2}[x] = (1/m)·F(t)
d_{t}[x] = (1/m)·int[ F(t) ]d[t]
x(t) = (1/m)·int-int[ F(t) ]d[t]d[t]
Deducción:
m·d_{tt}^{2}[x] = F(t)
d_{t}[x] = int[ d_{tt}^{2}[x] ]d[t] = int[ (1/m)·F(t) ]d[t] = (1/m)·int[ F(t) ]d[t]
x(t) = int[ d_{t}[x] ]d[t] = int[ (1/m)·int[ F(t) ]d[t] ]d[t] = (1/m)·int-int[ F(t) ]d[t]d[t]
Fumretzen-ten-dut-zû-tek més-nek tabaki-koak que ayere-dut.
Fumretzen-ten-dut-zû-tek ménus-nek tabaki-koak que ayere-dut.
Abans-nek dels déxum sisotzok,
no fumretzen-ten-dut-zava-tek
Després-nek dels déxum sisotzok,
fumretzen-ten-dut-zava-tek
Fumu-puesh mésh tabacu que ayere-dush
Fumu-puesh menush tabacu que ayere-dush
Abansh he-puesh compratu-dush,
un pernatúne-y de puerku.
Desprésh he-puesh compratu-dush,
un pernatúne-y de senglare-dush
Fumû més tabac que ahir
Fumû menys tabac que ahir
Constructor:
més [o] més-nek [o] mésh [o] méh
Destructor:
menys [o] ménus-nek [o] menush [o] menuh
Mi familia me está haciendo seguidores no siguiendo-me,
y no amar al próximo como a si mismo,
no vos quejéis si el mundo prójimo se cree que soy Jesucristo,
porque lo hacéis vosotros con vuestro rezo.
Se lo cree mucho el mundo que soy el mesías,
porque no es ninguien profeta en su tierra.
Teorema: [ fracción continua ]
2n = < 0,0,2n >
2n+1 = < 1,0,2n >
Clásico:
oveja [o] ovella
oreja [o] orella
ojo [o] ull
piojo [o] piull
Blindaje [o] Blindatjje
Rodaje [o] Rodatjje
Lenguaje [o] Llenguatjje
Hormaje [o] Formatjje [ Queso ]
Definición: [ de topología ]
[AD_{k}][ D_{k} € E ==> ( [ || ]-[k = 1]-[n][ D_{k} ] € E & [&]-[k = 1]-[n][ D_{k} ] € E ) ]
[A¬D_{k}][ ¬D_{k} € E ==> ( [&]-[k = 1]-[n][ ¬D_{k} ] € E & [ || ]-[k = 1]-[n][ ¬D_{k} ] € E ) ]
Definición: [ de morfismo-topológico ]
f( [ || ]-[k = 1]-[n][ D_{k} ] ) = [ || ]-[k = 1]-[n][ f(D_{k}) ]
f( [&]-[k = 1]-[n][ D_{k} ] ) = [&]-[k = 1]-[n][ f(D_{k}) ]
Teorema:
Sea ( E = { 0,D_{1},...(n)...,D_{n},A } & B = [ || ]-[k = 1]-[n][ D_{k} ] & B [<< A ) ==>
Si f(x) es un morfismo-topológico ==> ...
... f( interior[E] ) [ || ] f( exterior[E] ) = f(A).
Si f(x) es un morfismo-topológico ==> ...
... f( interior[E] ) [&] f( exterior[E] ) = f(0).
Demostración:
f( interior[E] ) = [ || ]-[k = 1]-[n][ f(D_{k}) ] = f( [ || ]-[k = 1]-[n][ D_{k} ] ) = f(B)
f( exterior[E] ) = [&]-[k = 1]-[n][ f(A [ \ ] D_{k}) ] = f( A [ \ ] [ || ]-[k = 1]-[n][ D_{k} ] ) = f(A [ \ ] B)
Base topológica:
B = [ || ]-[k = 1]-[n][ D_{k} ]
A [ \ ] B = [&]-[k = 1]-[n][ (A [ \ ] D_{k}) ]
C = [&]-[k = 1]-[n][ D_{k} ]
A [ \ ] C = [ || ]-[k = 1]-[n][ (A [ \ ] D_{k}) ]
Teorema:
Sea E = { 0,{x},{z,y},{x,y},{z},{x,y,z} }
Si f(x) es un morfismo-topológico ==> ...
... f( interior[E] ) [ || ] f( exterior[E] ) = f({x,y,z}).
Si f(x) es un morfismo-topológico ==> ...
... f( interior[E] ) [&] f( exterior[E] ) = f(0).
Demostración:
f( interior[E] ) = f({x}) [ || ] f({x,y}) = f({x,y})
f( exterior[E] ) = f({z,y}) [&] f({z}) = f({z})
Base topológica:
{x,y} = {x} [ || ] {x,y}
{z} = {z,y} [&] {z}
{x} = {x} [&] {x,y}
{y,z} = {z} [ || ] {z,y}
Teorema:
Sea E = { 0,[(-n),n]_{R},( ((-a),(-n))_{R} [ || ] (n,a)_{R} ),((-a),a)_{R} } & n < a
Si f(x) es un morfismo-topológico ==> ...
... f( interior[E] ) [ || ] f( exterior[E] ) = f(((-a),a)_{R}).
Si f(x) es un morfismo-topológico ==> ...
... f( interior[E] ) [&] f( exterior[E] ) = f(0).
Demostración:
( (-a) < x < (-n) < n < a || (-a) < (-n) [< x [< n < a || (-a) < (-n) < n < x < a ) ==> (-a) < x < a
Sea E = { 0,n,m,n+m }
Si f(x) es un morfismo-topológico ==> ...
... max{ f( interior[E] ),f( exterior[E] ) } = f(n+m).
Si f(x) es un morfismo-topológico ==> ...
... min{ f( interior[E] ),f( exterior[E] ) } = f(0).
Demostración:
f( interior[E] ) = max{ f(n),f(n+m) } = f(n+m)
f( exterior[E] ) = min{ f(m),f(0) } = f(0)
Base topológica:
n+m = max{ n,n+m }
0 = min{ m,0 }
n = min{ n,n+m }
m = max{ m,0 }
Sea E = { 0,(1/n),( 1+(-1)·(1/n) ),1 }
Si f(x) es un morfismo-topológico ==> ...
... max{ f( interior[E] ),f( exterior[E] ) } = f(1).
Si f(x) es un morfismo-topológico ==> ...
... min{ f( interior[E] ),f( exterior[E] ) } = f(0).
Demostración:
f( interior[E] ) = max{ f(1/n),f(1) } = f(1)
f( exterior[E] ) = min{ f(1+(-1)·(1/n)),f(0) } = f(0)
Base topológica:
1 = max{ (1/n),1 }
0 = min{ ( 1+(-1)·(1/n) ),0 }
(1/n) = min{ (1/n),1 }
( 1+(-1)·(1/n) ) = max{ ( 1+(-1)·(1/n) ),0 }
Compactificación de Alexandroff de los enteros:
Base topológica:
2p+1 = max{1,2p+1}
0 = min{0,2p}
1 = min{1,2p+1}
2p = max{0,2p}
[r]_{2m} = { p : [Ek][ p = (2m)·k+r ] } ==> ...
... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] = Z
[r]_{2m+1} = { p : [Ek][ p = (2m+1)·k+r ] } ==> ...
... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] [ || ] D_{r = 2m} = Z
Compactificación de Alexandroff de los polinomios:
2p+1 = max{1,2p+1}
0 = min{0,2p}
1 = min{1,2p+1}
2p = max{0,2p}
[r(x)]_{2m} = ...
... { P(x) : [Ek(x)][ P(x) = m(x)·k(x)+r(x) & grado(m(x)) = (2m) & grado(r(x)) = r ] } ==> ...
... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] = Z[x]
[r(x)]_{2m+1} = ...
... { P(x) : [Ek(x)][ P(x) = m(x)·k(x)+r(x) & grado(m(x)) = (2m+1) & grado(r(x)) = r ] } ==> ...
... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] [ || ] D_{r = 2m} = Z[x]
Compactificación de Alexandroff de los racionales:
Base topológica:
2p+1 = max{1,2p+1}
0 = min{0,2p}
1 = min{1,2p+1}
2p = max{0,2p}
[r]_{2m} = { (p/q) : [Ek][ (p/q) = (2m)·(k/q)+(r/q) ] } ==> ...
... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] = Q
[r]_{2m+1} = { (p/q) : [Ek][ (p/q) = (2m+1)·(k/q)+(r/q) ] } ==> ...
... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] [ || ] D_{r = 2m} = Q
Compactificación de Alexandroff de las fracciones polinómicas:
2p+1 = max{1,2p+1}
0 = min{0,2p}
1 = min{1,2p+1}
2p = max{0,2p}
[r(x)]_{2m} = ...
... { ( P(x)/Q(x) ) : [Ek(x)][ ( P(x)/Q(x) ) = m(x)·( k(x)/Q(x) )+( r(x)/Q(x) ) & ...
... grado(m(x)) = (2m) & grado(r(x)) = r ] } ==> ...
... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] = Q[x]
[r(x)]_{2m+1} = ...
... { ( P(x)/Q(x) ) : [Ek(x)][ ( P(x)/Q(x) ) = m(x)·( k(x)/Q(x) )+( r(x)/Q(x) ) & ...
... grado(m(x)) = (2m+1) & grado(r(x)) = r ] } ==> ...
... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] [ || ] D_{r = 2m} = Q[x]
Compactificación de Garriga-Alexandroff de los enteros:
Base topológica:
4p+3 = max{4p+1,4p+3}
4p = min{4p,4p+2}
4p+1 = min{4p+1,4p+3}
4p+2 = max{4p,4p+2}
[r]_{4m} = { p : [Ek][ p = (4m)·k+r ] } ==> ...
... [ || ]-[r = 0]-[4m+(-1)][ D_{r = 4p} [ || ] D_{r = 4p+2} [ || ] D_{r = 4p+1} [ || ] D_{r = 4p+3} ] = Q
[r]_{4m+1} = { p : [Ek][ p = (4m+1)·k+r ] } ==> ...
... [ || ]-[r = 0]-[4m+(-1)][ D_{r = 4p} [ || ] D_{r = 4p+2} [ || ] D_{r = 4p+1} [ || ] D_{r = 4p+3} ] ...
... [ || ] D_{4m} = Q
[r]_{4m+2} = { p : [Ek][ p = (4m+2)·k+r ] } ==> ...
... [ || ]-[r = 0]-[4m+(-1)][ D_{r = 4p} [ || ] D_{r = 4p+2} [ || ] D_{r = 4p+1} [ || ] D_{r = 4p+3} ] ...
... [ || ] D_{4m} [ || ] D_{4m+1} = Q
[r]_{4m+3} = { p : [Ek][ p = (4m+3)·k+r ] } ==> ...
... [ || ]-[r = 0]-[4m+(-1)][ D_{r = 4p} [ || ] D_{r = 4p+2} [ || ] D_{r = 4p+1} [ || ] D_{r = 4p+3} ] ...
... [ || ] D_{4m} [ || ] D_{4m+1} [ || ] D_{4m+2} = Q
Definición:[ de morfismo-topológico compacto ]
[EA][EB][ A = (a,b)_{R} & B = (¬b,¬a)_{R} & A [ || ] B = rec(f) ]
Teorema:
Si f(n) = n ==> f(n) es un morfismo-topológico compacto.
Demostración:
f(max{a_{1},...,a_{n}}) = max{a_{1},...,a_{n}} = max{f(a_{1}),...,f(a_{n})}
f(min{a_{1},...,a_{n}}) = min{a_{1},...,a_{n}} = min{f(a_{1}),...,f(a_{n})}
Base topológica:
0 = min{0,n}
n+1 = max{1,n+1}
1 = min{1,n+1}
n = max{0,n}
(0,n]_{R} [ || ] [1,n+1)_{R} [<< (0,oo)_{R}
Teorema:
Si f(n) = (1/n) ==> f(n) es un morfismo-topológico dual compacto.
Demostración:
f(max{a_{1},...,a_{n}}) = ( 1/max{a_{1},...,a_{n}} ) = min{(1/a_{1}),...,(1/a_{n})} =...
... min{f(a_{1}),...,f(a_{n})}
f(min{a_{1},...,a_{n}}) = ( 1/min{a_{1},...,a_{n}} ) = max{(1/a_{1}),...,(1/a_{n})} =...
... max{f(a_{1}),...,f(a_{n})}
Base topológica:
0 = min{0,( 1+(-1)·(1/n) )}
1 = max{1,(1/n)}
(1/n) = min{1,(1/n)}
( 1+(-1)·(1/n) ) = max{0,( 1+(-1)·(1/n) )}
[0,( 1+(-1)·(1/n) ]_{R} [ || ] [(1/n),1]_{R} [<< [0,1]_{R}
Teorema:
Si f(n) = n+p ==> f(n) es un morfismo-topológico compacto.
Demostración:
f(max{a_{1},...,a_{n}}) = max{a_{1},...,a_{n}}+p = max{a_{1}+p,...,a_{n}+p} = ...
... max{f(a_{1}),...,f(a_{n})}
f(min{a_{1},...,a_{n}}) = min{a_{1},...,a_{n}}+p = min{a_{1}+p,...,a_{n}+p} = ...
... min{f(a_{1}),...,f(a_{n})}
Base topológica:
p = min{p,n+p}
(n+p)+1 = max{p+1,(n+p)+1}
p+1 = min{p+1,(n+p)+1}
n+p = max{p,n+p}
(p,n+p]_{R} [ || ] [p+1,(n+p)+1)_{R} [<< (p,oo)_{R}
Teorema:
Si f(n) = (1/n)+p ==> f(n) es un morfismo-topológico dual no compacto.
Demostración:
f(max{a_{1},...,a_{n}}) = ( 1/max{a_{1},...,a_{n}} )+p = min{(1/a_{1}),...,(1/a_{n})}+p = ...
min{(1/a_{1})+p,...,(1/a_{n})+p )} = min{f(a_{1}),...,f(a_{n})}
f(min{a_{1},...,a_{n}}) = ( 1/min{a_{1},...,a_{n}} )+p = max{(1/a_{1}),...,(1/a_{n})}+p = ...
max{(1/a_{1})+p,...,(1/a_{n})+p} = max{f(a_{1}),...,f(a_{n})
rec(f) = [p,p+1]_{R} & [En][ n = 1 & rec(f) = [p,(-p)]_{R} [ || ] [p+1,p+1]_{R} ]
Teorema:
No es ninguien profeta en su tierra, siendo un Peráclito
porque quizás lo hacen Peráclito,
saltando-se algún mandamiento como el ama al próximo como a ti mismo.
Demostración:
Es alguien profeta en su tierra, no siendo un Peráclito
aunque lo hacen Peráclito,
saltando-se algún mandamiento como el ama al próximo como a ti mismo.
Ley:
Si t = d·( ( 1/(d_{t}[x]+v) )+( 1/(d_{t}[x]+(-v)) ) ) ==>
d_{t}[x] = (1/t)·( d+( d^{2}+(tv)^{2} )^{(1/2)} )
x(t) = ln(t) [o(t)o] ( dt+( (1/3)·( d^{2}+(tv)^{2} )^{(3/2)} [o(t)o] (1/v)^{2}·ln(t) ) )
d_{tt}^{2}[x] = (-1)·(1/t)^{2}·( d+( d^{2}+(tv)^{2} )^{(1/2)} )+v^{2}·( d^{2}+(tv)^{2} )^{(-1)·(1/2)}
Ley:
F(u,x) = a·mc^{2}·S(u)·(ax)^{n}
F(v,x) = a·mc^{2}·S(v)·(ax)^{n}
E(u,x) = mc^{2}·int[S(u)]d[u] [o(u)o] ( 1/(n+1) )·(ax)^{n+1}
E(v,x) = mc^{2}·int[S(v)]d[v] [o(v)o] ( 1/(n+1) )·(ax)^{n+1}
Ley:
F(u,x) = mc^{2}·S(u)·(1/x)
F(v,x) = mc^{2}·S(v)·(1/x)
E(u,x) = mc^{2}·int[S(u)]d[u] [o(u)o] ln(x)
E(v,x) = mc^{2}·int[S(v)]d[v] [o(v)o] ln(x)
Ley: [ de cuerda hetero-tópica de métrica básica ]
Si ( S(u) = (1/4)·e^{2it·u} & S(v) = (1/4)·e^{2it·v} ) ==>
E(u,x) = mc^{2}·(1/8)·(1/(it))·e^{2it·u} [o(u)o] ( 1/(n+1) )·(ax)^{n+1}
E(v,x) = mc^{2}·(1/8)·(1/(it))·e^{2it·v} [o(v)o] ( 1/(n+1) )·(ax)^{n+1}
Ley: [ de cuerda elíptica de métrica básica ]
Si ( S(u) = (1/2)·( (n+1)/(2n+1) )·(tu)^{2n+2} & S(v) = (1/2)·( (n+1)/(2n+1) )·(tu)^{2n+2} ) ==>
E(u,x) = mc^{2}·(1/2)·( (n+1)/(4n^{2}+8n+3) )·(1/t)·(tu)^{2n+3} [o(u)o] ( 1/(n+1) )·(ax)^{n+1}
E(v,x) = mc^{2}·(1/2)·( (n+1)/(4n^{2}+8n+3) )·(1/t)·(tv)^{2n+3} [o(v)o] ( 1/(n+1) )·(ax)^{n+1}
Definición:
( f(ax) )^{n}+1 = ( f(ax) )^{[n]}
Teorema:
( f(ax) )^{n}+( f(ax) )^{m} = ( f(ax) )^{m}·( ( f(ax) )^{n+(-m)}+1 ) = ...
... ( f(ax) )^{m}·( f(ax) )^{[n+(-m)]} = ( f(ax) )^{m+[n+(-m)]}
Ley:
Si d_{t}[x] = v·( (ax)^{n}+1 ) ==>
x(t) = (1/a)·( ( (-1)·[n]+1 )·avt )^{( 1/( (-1)·[n]+1 ) )}
d_{t}[x] = v·( ( (-1)·[n]+1 )·avt )^{( [n]/( (-1)·[n]+1 ) )}
d_{tt}^{2}[x] = av^{2}·[n]·( ( (-1)·[n]+1 )·avt )^{( ( 2·[n]+(-1) )/( (-1)·[n]+1 ) )}
Ley:
Si d_{t}[x] = v·( (ax)^{n}+(ax)^{m} ) ==>
x(t) = (1/a)·( ( (-1)·(m+[n+(-m)])+1 )·avt )^{( 1/( (-1)·(m+[n+(-m)])+1 ) )}
d_{t}[x] = v·( ( (-1)·(m+[n+(-m)])+1 )·avt )^{( (m+[n+(-m)])/( (-1)·(m+[n+(-m)])+1 ) )}
d_{tt}^{2}[x] = av^{2}·(m+[n+(-m)])·...
... ( ( (-1)·(m+[n+(-m)])+1 )·avt )^{( ( 2·(m+[n+(-m)])+(-1) )/( (-1)·(m+[n+(-m)])+1 ) )}
Ley:
Si d_{t}[x] = v·( e^{nax}+1 ) ==>
x(t) = (1/a)·(1/[n])·(-1)·ln( (-1)·[n]·avt )
d_{t}[x] = (1/a)·(1/[n])·(-1)·(1/t)
d_{tt}^{2}[x] = (1/a)·(1/[n])·(1/t)^{2}
Ley:
Si d_{t}[x] = v·( e^{nax}+e^{max} ) ==>
x(t) = (1/a)·( 1/(m+[n+(-m)]) )·(-1)·ln( (-1)·(m+[n+(-m)])·avt )
d_{t}[x] = (1/a)·( 1/(m+[n+(-m)]) )·(-1)·(1/t)
d_{tt}^{2}[x] = (1/a)·( 1/(m+[n+(-m)]) )·(1/t)^{2}
Ley: [ del abrazo al cojín ]
z(x) = < 1,1,x,(1/x) > es un placer
z(x) = < 1,1,(-x),(-1)·(1/x) > es un placer
(1/x) = brazo derecho adalto y brazo izquierdo abajo.
(-1)·(1/x) = brazo derecho abajo y brazo izquierdo adalto.
Ley: [ de sexo de chocho ]
z(x) = < (1/n),2e^{ix},2e^{(-1)·ix},n·(1/4) > es un placer
Con más de n = 4,
de polla = 0111-111111,
de chocho 111-1110111-111
ya no hay placer en ser el símbolo > 1
Ley: [ de sexo de culo ]
z(x) = < (-n),2e^{ix},2e^{(-1)·ix},n+(-4)·cos(x) > es un dolor
Con más de n = 4,
5 violaciones,
ya no hay dolor en ser el símbolo > 0
