matemátiques y dualogía y rotació y transitius duals borrosos

Teorema:

Si a_{n+1} >] a_{n}+n ==> a_{n+1} >] a_{n}

Si a_{n+1} < a_{n}+(-n)+(-1) ==> a_{n+1} < a_{n}

Demostració:

a_{n+1} >] a_{n}+n >] a_{n}

a_{n+1} < a_{n}+(-n)+(-1) < a_{n}

Teorema:

Si a_{n+1} [< a_{n}+(-n) ==> a_{n+1} [< a_{n}

Si a_{n+1} > a_{n}+n+1 ==> a_{n+1} > a_{n}

Demostració:

a_{n+1} [< a_{n}+(-n) [< a_{n}

a_{n+1} > a_{n}+n+1 > a_{n}

Teorema:

d_{x}[y] = f(x)·y

y(x) = e^{int[f(x)]d[x]}

d_{x}[y] = (1/f(x))·y

y(x) = e^{( int[f(x)]d[x] )^{[o(x)o](-1)}}

Teorema:

d_{x}[y] = f(x)·y^{n}

y(x) = ( int[f(x)]d[x] )^{( 1/(1+(-n)) )}

d_{x}[y] = (1/f(x))·y^{n}

y(x) = ( ( int[f(x)]d[x] )^{[o(x)o](-1)} )^{( 1/(1+(-n)) )}

Teorema:

d_{x}[y] = ( ax^{2}+bx+c )^{m}·y^{n}

y(x) = ( ...

... (1/(m+1))·( ax^{2}+bx+c )^{m+1} [o(x)o] ...

... ln(2ax+b) [o(x)o] (1/(2a))·x ...

... )^{( 1/(1+(-n)) )}

d_{x}[y] = ( 1/( ax^{2}+bx+c )^{m} )·y^{n}

y(x) = ( ...

... ( (1/(m+1))·( ax^{2}+bx+c )^{m+1} [o(x)o] ...

... ln(2ax+b) [o(x)o] (1/(2a))·x )^{[o(x)o](-1)} ...

... )^{( 1/(1+(-n)) )}

Sexo en lo borroso:

Polla virgen:

0111 = (1/3)

Chocho virgen:

1110111 = (2/3)

Lo siguiente no sé si funciona en la Tierra:

Polla no virgen + Chocho virgen:

0111-11-11 + 1110111 = 0111 = (1/4)

Polla virgen + Chocho no virgen:

0111 + 11-1110111-11 = 0111 = (1/4)

Polla no virgen + Chocho no virgen:

0111-11-11 + 11-1110111-11 = 11 = (3/4)

Dualogía:

Definició:

Sigui x+y(x) = f(x) & [Ex_{k}][ f(x_{k}) = 0 ] ==> ...

... Dual( f(x) ) = {< x_{1},y(x_{1}) >,...(n)...,< x_{n},y(x_{n}) >}

Teorema:

x+y(x) = x+(-a) <==> Dual(x+(-a)) = {< a,(-a) >}

x+y(x) = x+a <==> Dual(x+a) = {< (-a),a >}

Dual(x+(-a)) [ || ] Dual(x+a) es simétrica

Teorema:

x+y(x) = x^{2}+(-a) <==> ...

... Dual(x^{2}+(-a)) = {< a^{(1/2)},(-1)·a^{(1/2)} >,< (-1)·a^{(1/2)},a^{(1/2)} >}

x+y(x) = x^{2}+a <==> ...

... Dual(x^{2}+a) = {< ia^{(1/2)},(-i)·a^{(1/2)} >,< (-i)·a^{(1/2)},ia^{(1/2)} >}

Dual(x^{2}+(-a)) es simétrica

Dual(x^{2}+a) es simétrica

Teorema:

x+y(x) = x^{3}+(-a) <==> ...

... Dual(x^{3}+(-a)) = {< (-u)·a^{(1/3)},ua^{(1/3)} >,< (-v)·a^{(1/3)},va^{(1/3)} >,...

... < a^{(1/3)},(-1)·a^{(1/3)} >}

x+y(x) = x^{3}+a <==> ...

... Dual(x^{3}+a) = {< ua^{(1/3)},(-u)·a^{(1/3)} >,< va^{(1/3)},(-v)·a^{(1/3)} >,...

... < (-1)·a^{(1/3)},a^{(1/3)} >}

Dual(x^{3}+(-a)) [ || ] Dual(x^{3}+a) es simétrica

Teorema:

x+y(x) = x^{4}+(-a) <==> ...

... Dual(x^{4}+(-a)) = {< a^{(1/4)},(-1)·a^{(1/4)} >,< (-1)·a^{(1/4)},a^{(1/4)} >,...

... < ia^{(1/4)},(-i)·a^{(1/4)} >,< (-i)·a^{(1/4)},ia^{(1/4)} >}

x+y(x) = x^{4}+a <==> ...

... Dual(x^{4}+a) = {< ja^{(1/4)},(-j)·a^{(1/4)} >,< (-j)·a^{(1/4)},ja^{(1/4)} >,...

... < ka^{(1/4)},(-k)·a^{(1/4)} >,< (-k)·a^{(1/4)},ka^{(1/4)} >}

Dual(x^{4}+(-a)) es simétrica

Dual(x^{4}+a) es simétrica

Definició:

Sigui x+y(x) = f(x) & [Ex_{k}][ d_{x}[f(x_{k})] = 1 ] ==> ...

... Dual-d_{x}[f(x)] = {< x_{1},y(x_{1}) >,...(n)...,< x_{n},y(x_{n}) >}

Teorema:

x+y(x) = x+(-a) <==> Dual-d_{x}[x+(-a)] = {< b,(-a) >}

x+y(x) = x+a <==> Dual-d_{x}[x+a] = {< b,a >}

Teorema:

x+y(x) = (1/2)·x^{2}+(-a) <==> ...

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

x+y(x) = (1/2)·x^{2}+a <==> ...

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

Teorema:

x+y(x) = (1/(n+1))·x^{n+1}+(-a) <==> ...

... Dual-d_{x}[(1/(n+1))·x^{n+1}+(-a)] = ...

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

x+y(x) = (1/(n+1))·x^{n+1}+a <==> ...

... Dual-d_{x}[(1/(n+1))·x^{n+1}+a] = ...

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

Mecánica de rotació:

Lley:

Sigui d_{tt}^{2}[w] = 0 ==> ...

... Si ( d_{t}[y] = a·y(t) & d_{t}[x] = d_{t}[y]+(d_{t}[w]/w)·y(t) ) ==> ...

... d_{tt}^{2}[x] = ( a^{2}+(-1)·(d_{t}[w]/w)^{2} )·y(t)+(d_{t}[w]/w) )·a·y(t)

Sigui d_{tt}^{2}[w] = 0 ==> ...

... Si ( d_{t}[y] = b·y(t) & d_{t}[x] = d_{t}[y]+(-1)·(d_{t}[w]/w)·y(t) ) ==> ...

... d_{tt}^{2}[x] = ( b^{2}+(d_{t}[w]/w)^{2} )·y(t)+(-1)·(d_{t}[w]/w) )·b·y(t)

Lley:

Sigui w = e^{at} ==> ...

... [1] x = y+at [o(t)o] int[ r(t) ]d[t]

... [2] d_{t}[x] = d_{t}[y]+a·r(t)

... [3] d_{tt}^{2}[x] = d_{tt}^{2}[y]+a·d_{t}[r(t)]

Sigui w = e^{(-1)·at} ==> ...

... [1] x = y+(-1)·at [o(t)o] int[ r(t) ]d[t]

... [2] d_{t}[x] = d_{t}[y]+(-a)·r(t)

... [3] d_{tt}^{2}[x] = d_{tt}^{2}[y]+(-a)·d_{t}[r(t)]

A r(t) = constant:

és inercial

A r(t) != constant:

no és inercial

Lley:

Sigui w = cosh(at) ==> ...

... [1] x = y+( [2at]+(-1)·( at+ln(2) ) ) [o(t)o] int[ r(t) ]d[t]

... [2] d_{t}[x] = d_{t}[y]+a·tanh(at)·r(t)

... [3] d_{tt}^{2}[x] = ...

... d_{tt}^{2}[y]+a^{2}·(1+(-1)·( tanh(at) )^{2} )·r(t)+a·tanh(at)·d_{t}[r(t)]

Sigui w = sinh(at) ==> ...

... [1] x = y+( ]2at[+(-1)·( at+ln(2) ) ) [o(t)o] int[ r(t) ]d[t]

... [2] d_{t}[x] = d_{t}[y]+a·coth(at)·r(t)

... [3] d_{tt}^{2}[x] = ...

... d_{tt}^{2}[y]+a^{2}·(1+(-1)·( coth(at) )^{2} )·r(t)+a·coth(at)·d_{t}[r(t)]

Deducció:

cosh(at) = (1/2)·( e^{at}+e^{(-1)·at} ) = (e^{at}/e^{ln(2)+at})·(e^{at}+e^{(-1)at})

sinh(at) = (1/2)·( e^{at}+(-1)·e^{(-1)·at} ) = (e^{at}/e^{ln(2)+at})·(e^{at}+(-1)·e^{(-1)at})

cosh(at) = (1/e^{ln(2)+at})·( e^{2at}+1 ) = e^{[2at]+(-1)·( at+ln(2) )}

sinh(at) = (1/e^{ln(2)+at})·( e^{2at}+(-1) ) = e^{]2at[+(-1)·( at+ln(2) )}

Teoremes dual transitius borrosos:

Teorema:

( x [< y_{n} & y_{n} [< y_{n+k} ) <==> x [< y_{n+k}

( x > y_{n} || y_{n} > y_{n+k} ) <==> x > y_{n+k}

Demostració:

min({(0.n)+(0.k)}) [< (0.n+k)

sup({(-1)·(0.n)+(-1)·(0.k)}) > (-1)·(0.n+k)

Teorema:

( x >] y_{n} & y_{n} >] y_{n+k} ) <==> x >] y_{n+k}

( x < y_{n} || y_{n} < y_{n+k} ) <==> x < y_{n+k}

Demostració:

max({(-1)·(0.n)+(-1)·(0.k)}) >] (-1)·(0.n+k)

inf({(0.n)+(0.k)}) < (0.n+k)

Teorema:

( x = x & x [< y_{n} ) <==> x [< y_{n}

( x != x || x > y_{n} ) <==> x > y_{n}

Demostració:

min({1,(0.n)}) [< (0.n)

sup({(-1),(-1)·(0.n)}) > (-1)·(0.n)

Teorema:

( x = x & x >] y_{n} ) <==> x >] y_{n}

( x != x || x < y_{n} ) <==> x < y_{n}

Demostració:

max({(-1),(-1)·(0.n)}) >] (-1)·(0.n)

inf({1,(0.n)}) < (0.n)

Teorema:

( y_{n} [< x & x = x ) <==> y_{n} [< x

( y_{n} > x || x != x ) <==> y_{n} > x

Demostració:

max({(-1)·(0.n),(-1)}) >] (-1)·(0.n)

inf({(0.n),1}) < (0.n)

Teorema:

( y_{n} >] x & x = x ) <==> y_{n} >] x

( y_{n} < x || x != x ) <==> y_{n} < x

Demostració:

min({(0.n),1}) [< (0.n)

sup({(-1)·(0.n),(-1)}) > (-1)·(0.n)

Rotació:

s(t) = w(t)·r

d_{t}[s] = d_{t}[w]·r

d_{tt}^{2}[s] = d_{tt}^{2}[w]·r

(m/2)·d_{t}[s]^{2} = (m/2)·d_{t}[w]^{2}·r^{2}

Lley:

d_{tt}^{2}[s] = a·pi·r

d_{t}[s] = a·t·pi·r

s(t) = a·(1/2)·t^{2}·pi·r

(m/2)·d_{t}[s]^{2} = m·a·pi·r·s

Lley:

d_{tt}^{2}[s] = (-a)·pi·r

d_{t}[s] = (-a)·t·pi·r

s(t) = (-a)·(1/2)·t^{2}·pi·r

(m/2)·d_{t}[s]^{2} = m·(-a)·pi·r·s