hyper-espai

x(t) = ( c^{n+(-1)}/l^{n+(-1)} )·Vt^{n}

l^{n+(-1)} = ona de (n+(-1)) hiper-espais de retorn a l'espai.

x(t) = ( c^{n+(-1)}/l^{n+(-1)} )·d_{t}[x]·t^{n}

x(t) = e^{ ( ( l^{n+(-1)}/c^{n+(-1)})·( 1/((-n)+1) )·t^{(-n)+1} }

parts de naturals

oo [x] ...(oo)... [x] oo <---> {n_{1},2^{n_{2}},...,m^{n_{m}},...}

1+2+...+2^{n}+oo^{oo} = oo^{oo}

cardinal de P(N) = oo^{oo}

no elements

{. ._{x}} <==> {x}

}. ._{x}{ <==> }x{

f(. ._{x}) = f(. ._{y})

x = y

{. ._{x},. ._{y}} <==> {x,y}

}. ._{x},. ._{y}{ <==> }x,y{

{. ._{1},...,. ._{n}} <==> {1,...,n}

}. ._{1},...,. ._{n}{ <==> }1,...,n{

{. ._{(-1)},...,. ._{(-n)}} <==> {(-1),...,(-n)}

}. ._{(-1)},...,. ._{(-n)}{ <==> }(-1),...,(-n){

[A. ._{x}][ . ._{x}€. ._{V} ] & . ._{V} = {. ._{x} : . ._{x} = . ._{x}}

[A. ._{x}][ ¬( . ._{x}€. ._{0} ) ] & . ._{0} = {. ._{x} : . ._{x} != . ._{x}}

energía numerable

valoració de pensament

(n/m)+((m+(-n))/m) = 1

< m·oo <---> oo & ( mk+j <--> k ) >

mp+j = mq+j

mp = mq

p = q

< oo^{n} <---> oo & ( k2^{k}...n^{k} <--> k ) >

p2^{p}...n^{p} = q2^{q}...n^{q}

p = q & 2^{p} = 2^{q} & ...& n^{p} = n^{q}

p = q & p = q & ... & p = q

p = q

< oo^{m·oo} <---> oo^{oo} & ( oo^{mk+j} <--> oo^{k} ) >

oo^{mp+j} = oo^{mq+j}

mp+j = mq+j

mp = mq

p = q

lagranià de cordes

corda tub:

L(x,u,v) = a·x(u,v)+(-1)·h·( e^{iu}+e^{iv} )

constructor

d_{u}[L(x,u,v)] = a·d_{u}[x(u,v)]+(-1)·ih·e^{iu}

d_{v}[L(x,u,v)] = a·d_{v}[x(u,v)]+(-1)·ih·e^{iv}

x(u,v) = (h/a)·e^{iu}+(h/a)·e^{iv}

destructor:

d_{u}[x(u,v)] = (a/(hi))·e^{(-i)u}

d_{v}[x(u,v)] = (a/(hi))·e^{(-i)v}

x(u,v) = (a/h)·e^{(-i)u}+(a/h)·e^{(-i)v}

corda arc:

L(x,y,u,v) = (1/2)·a·( ( x(u) )^{2}+( y(v) )^{2} )+(e^{iu}+(-1)·e^{iv})·( e^{iu}+e^{iv} )

constructor

d_{u}[L(x,y,u,v)] = (1/2)·a·d_{u}[( x(u) )^{2}]+i·e^{2iu}

d_{v}[L(x,y,u,v)] = (1/2)·a·d_{v}[( y(v) )^{2}]+(-i)·e^{2iv}

x(u) = (1/a)^{(1/2)}·(j/i)·e^{iu}

y(v) = (1/a)^{(1/2)}·(k/i)·e^{iv}