[En][ ( n+(1/(n+1)) ) [< (3/2) ]
Exposición:
n = 1
f(n) = 0
1 = ( f(n)+(1/(f(n)+1)) ) = ( n+(1/(n+1)) ) < (3/2)
Arte:
[En][ ( 2n+(1/(2n+1)) ) [< (7/3) ]
Traumatología vertebral:
Principio:
Amisnostrofia resistiva:
[ER][ R(t) >] 1 & W = R(t)·d_{t}[q] ]
Principio:
Aminostrofia condensativa:
[EC][ 0 [< C(t) [< 1 & W = C(t)·q(t) ]
Traumatología sanguínea:
Principio:
Trompo de colesterol:
Sea K es cabal sanguíneo ==>
[ES][ S(t) >] 1 & K = S(t)·d_{t}[x] ]
Principio:
Trompo de obstrucción de arteria:
Sea K es cabal sanguíneo ==>
[ES][ S(t) >] 1 & K = S(t)·ux ]
Oncología de transporte de intestino:
Principio:
Flojura de estómago:
Sea d_{xyz}^{3}[m(x,y,z,t)] la densidad del cagado ==>
[EM][ (M(t)/K) = int[ d_{xyz}^{3}[m(x,y,z,t)] ]d[t] ]
Principio:
Dureza de riñón:
Sea d_{xyz}^{3}[m(x,y,z,t)] la densidad del pijado ==>
[EM][ (M(t)/K) = int[ d_{xyz}^{3}[m(x,y,z,t)] ]d[t] ]
Ley:
Sea d_{xyz}^{3}[m(x,y,z,t)] = ma^{3} ==>
M(t) = mKa^{3}·t
m(x,y,z,t) = maxayaz
Ley:
Sea t >] (1/u) ==>
Si ( ( Si vt >] 1 ( retortijón ) ==> z(t) = vt ) & d_{xyz}^{3}[m(x,y,z,t)] = ma^{2}·(1/z)·(ut) ) ==>
M(t) = mKa^{2}·(1/v)·(ut)
m(x,y,z,t) = maxay·(ut)
Deducción:
d[z] = v·d[t]
d[x]d[y]d[z] = v·d[x]d[y]d[t]
Ley:
Sea t >] (1/u) ==>
Si ( ( Si vt >] 1 ( retortijón ) ==> z(t) = vt ) & d_{xyz}^{3}[m(x,y,z,t)] = ma^{4}·z·(1/(ut)) ) ==>
M(t) = mKa^{4}·v·(1/u)·t
m(x,y,z,t) = maxay·(av)^{2}·(1/u)·t
Deducción:
d[z] = v·d[t]
d[x]d[y]d[z] = v·d[x]d[y]d[t]
Ley:
Sea t >] (1/u) ==>
Si ( ( Si vt >] 1 ==> z(t) = vt ) & d_{xyz}^{3}[m(x,y,z,t)] = ma^{2}·(1/z)·(1/2)·(1+(ut)) ) ==>
M(t) = mKa^{2}·(1/(2v))·( ln(ut)+ut )
m(x,y,z,t) = maxay·(1/2)·( ln(ut)+ut )
Ley:
Sea t >] (1/u) ==>
Si ( ( Si vt >] 1 ==> z(t) = vt ) & d_{xyz}^{3}[m(x,y,z,t)] = ma^{4}·2z·( 1/(1+(ut)) ) ) ==>
M(t) = mKa^{4}·((2v)/u)·( ln(1+ut) [o(ut)o] (1/2)·(ut)^{2} )
m(x,y,z,t) = maxay·2·(av)^{2}·(1/u)^{2}·( ln(1+ut) [o(ut)o] (1/2)·(ut)^{2} )
Teoría del Falsus Infinitorum:
Axioma:
Si [Ej][ lim[n = j][ a_{n} ] = a & f(j) = m & g(m) = oo ] ==> ¬( lim[n = g(f(j))][ a_{n} ] = a )
Teoría del Falsus Algebratorum:
Axioma:
Si [Aj][ lim[n = j][ a_{n} ] != a & f(j) = m & g(m) = oo ] ==> ¬( lim[n = g(f(j))][ a_{n} ] = a )
Euler Falsus Infinitorum:
Arte:
sum[k = 0]-[oo][ ( 1/(k+1) )^{m} ] = (1/2)^{m}
Exposición:
lim[n = 1][ sum[k = 0]-[n][ ( 1/(k+1) )^{m} ]+(-1)·(1/n) ] = 1+(1/2)^{m}+(-1) = (1/2)^{m}
Arte:
sum[k = 1]-[oo][ ( 1/ln(k+1) )^{m}+(-1)·(1/k) ] = ( 1/ln(2) )^{m}
Exposición:
lim[n = 1][ sum[k = 1]-[n][ ( 1/ln(k+1) )^{m}+(-1)·(1/k) ]+(1/n) ] = ...
... ( 1/ln(2) )^{m}+(-1)+1 = ( 1/ln(2) )^{m}
Arte:
sum[k = 1]-[oo][ ( ln((1/k)+1) )^{m}+(-1)·(1/k) ] = ( ln(2) )^{m}
Exposición:
lim[n = 1][ sum[k = 1]-[n][ ( ln((1/k)+1) )^{m}+(-1)·(1/k) ]+(1/n) ] = ...
... ( ln(2) )^{m}+(-1)+1 = ( ln(2) )^{m}
Arte:
Prod[k = 1]-[oo][ (1/(2p))^{k}+( 1/(k+1) )^{m} ] = (1/p)+(1/2)^{m+(-1)}
Exposición:
lim[n = 1][ Prod[k = 1]-[n][ (1/(2p))^{k}+( 1/(k+1) )^{m} ]·(1+(1/n)) ] = ...
... ( (1/(2p))+(1/2)^{m} )·2 = (1/p)+(1/2)^{m+(-1)}
Arte:
Prod[k = 0]-[oo][ (1/(4p))^{k}+( 1/(k+1) )^{m} ] = (1/p)+(1/2)^{m+(-2)}
Exposición:
lim[n = 1][ Prod[k = 0]-[n][ (1/(4p))^{k}+( 1/(k+1) )^{m} ]·(1+(1/n)) ] = ...
... ( (1/(4p))+(1/2)^{m} )·4 = (1/p)+(1/2)^{m+(-2)}
Arte:
Prod[k = 1]-[oo][ m·( 1/(k+1) ) ] = m
Exposición:
lim[n = 1][ Prod[k = 1]-[n][ m·( 1/(k+1) ) ]·(1+(1/n)) ] = ( m·(1/2) )·2 = m
Arte:
Prod[k = 0]-[oo][ m·( 1/(k+1) ) ] = m^{2}
Exposición:
lim[n = 1][ Prod[k = 0]-[n][ m·( 1/(k+1) ) ]·(1+(1/n)) ] = m·( m·(1/2) )·2 = m^{2}
Ramanujan Falsus Infinitorum:
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(2)·sum[k = 1]-[oo][ 17·(1/k)^{2}+(-11)·(1/k)^{3} ]·(1/13) = pi^{2}
Exposición:
lim[n = 1][ Z(2)·sum[k = 1]-[n][ 17·(1/k)^{2}+(-11)·(1/k)^{3} ]·(1/13)+(12/13)·(1/n)·pi^{2} ] = ...
... Z(2)·(6/13)+(12/13)·pi^{2} = pi^{2}
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(2)·sum[k = 1]-[oo][ 47·(1/k)^{2}+(-41)·(1/k)^{3} ]·(1/43) = pi^{2}
Exposición:
lim[n = 1][ Z(2)·sum[k = 1]-[n][ 47·(1/k)^{2}+(-41)·(1/k)^{3} ]·(1/43)+(42/43)·(1/n)·pi^{2} ] = ...
... Z(2)·(6/43)+(42/43)·pi^{2} = pi^{2}
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(4)·sum[k = 1]-[oo][ 113·(1/k)^{4}+(-23)·(1/k)^{5} ]·(61/71) = pi^{4}
Exposición:
lim[n = 1][ Z(4)·sum[k = 1]-[n][ 113·(1/k)^{4}+(-23)·(1/k)^{5} ]·(61/71)+(10/71)·(1/n)·pi^{4} ] = ...
... Z(4)·90·(61/71)+(10/71)·pi^{4} = pi^{4}
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(4)·sum[k = 1]-[oo][ 101·(1/k)^{4}+(-11)·(1/k)^{5} ]·(43/73) = pi^{4}
Exposición:
lim[n = 1][ Z(4)·sum[k = 1]-[n][ 101·(1/k)^{4}+(-11)·(1/k)^{5} ]·(43/73)+(30/73)·(1/n)·pi^{4} ] = ...
... Z(4)·90·(43/73)+(30/73)·pi^{4} = pi^{4}
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(2)·sum[k = 1]-[oo][ ( (4k)!/k! )·( (53k+1)/216^{k} ) ]·(17/71) = pi^{2}
Exposición:
lim[n = 1][ Z(2)·sum[k = 1]-[n][ ( (4k)!/k! )·( (53k+1)/216^{k} ) ]·(17/71)+...
... (54/71)·(1/n)·pi^{2} ] = Z(2)·4!·54·(1/(4·54))·(17/71)+(54/71)·pi^{2} = pi^{2}
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(2)·sum[k = 1]-[oo][ ( (4k)!/k! )·( (73k+(-1))/288^{k} ) ]·(19/91) = pi^{2}
Exposición:
lim[n = 1][ Z(2)·sum[k = 1]-[n][ ( (4k)!/k! )·( (73k+(-1))/288^{k} ) ]·(19/91)+...
... (72/91)·(1/n)·pi^{2} ] = Z(2)·4!·72·(1/(4·72))·(19/91)+(72/91)·pi^{2} = pi^{2}
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(s) = (9/2)·Z(s)·sum[k = 1]-[oo][ e^{(-3)·pi·(k+(-1))} ]+
... (-2)·Z(s)·sum[k = 1]-[oo][ e^{(-2)·pi·(k+(-1))} ]+...
... (-1)·(1/2)·Z(s)·sum[k = 1]-[oo][ e^{(-pi)·(k+(-1))} ]
Exposición:
lim[n = 1][ (9/2)·Z(s)·sum[k = 1]-[n][ e^{(-3)·pi·(k+(-1))} ]+...
... (-2)·Z(s)·sum[k = 1]-[n][ e^{(-2)·pi·(k+(-1))} ]+...
... (-1)·(1/2)·Z(s)·sum[k = 1]-[n][ e^{(-pi)·(k+(-1))} ]+(-1)·Z(s)·(1/n) ] = Z(s)
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(s) = (31/8)·Z(s)·sum[k = 1]-[oo][ e^{(-31)·pi·(k+(-1))} ]+...
... (-2)·Z(s)·sum[k = 1]-[oo][ e^{(-2)·pi·(k+(-1))} ]+...
... (1/8)·Z(s)·sum[k = 1]-[oo][ e^{(-pi)·(k+(-1))} ]
Arte:
( 1+sum[k = 1]-[oo][ k·cos(k+(-1)) ] )^{(-2)}+( 1+sum[k = 1]-[oo][ k·cosh(k+(-1)) ] )^{(-2)} = 1
Exposición:
lim[n = 1][ ( 1+sum[k = 1]-[n][ k·cos(k+(-1)) ] )^{(-2)}+...
... ( 1+sum[k = 1]-[n][ k·cosh(k+(-1)) ] )^{(-2)}+(1/(2n)) ] = 1
Arte:
( 1+sum[k = 1]-[oo][ k·( 1/(k+(-1)) )·sin(k+(-1)) ] )^{(-2)}+...
... ( 1+sum[k = 1]-[oo][ k·( 1/(k+(-1)) )·sinh(k+(-1)) ] )^{(-2)} = 1
Arte:
Frac[k = 0]-[oo][ ( k!/(1+(k+1)!) ) ] = 1
Exposición:
lim[n = 0][ Frac[k = 0]-[n][ ( k!/(1+(k+1)!) ) ]·( 1+(1/(n+1)) ) ] = 1
Arte:
Frac[k = 0]-[oo][ ( (2k+1)/(1+(2k+3)) ) ] = (1/2)
Arte:
Frac[k = 1]-[oo][ ( (2k)/(1+(2k+2)) ) ] = (4/5)
Arte:
ln( Frac[k = 0]-[oo][ ( (e^{(-k)}+(-k))/(1+e^{(-1)·(k+1)}+(-1)·(k+1)) ) ] ) = ln(2)+1
Exposición:
lim[n = 0][ ...
... ln( Frac[k = 0]-[n][ ( (e^{(-k)}+(-k))/(1+e^{(-1)·(k+1)}+(-1)·(k+1)) ) ]·( 1+(1/(n+1)) ) ) ] = ...
.. ln(2e) = ln(2)+ln(e) = ln(2)+1
Arte:
ln( Frac[k = 0]-[oo][ ( (e^{(-k)·pi}+(-k))/(1+e^{(-1)·(k+1)·pi}+(-1)·(k+1)) ) ] ) = ln(2)+pi
Exposición:
lim[n = 0][ ...
... ln( Frac[k = 0]-[n][ ( (e^{(-k)·pi}+(-k))/(1+e^{(-1)·(k+1)·pi}+(-1)·(k+1)) ) ]·( 1+(1/(n+1)) ) ) ] = ...
... ln(2e^{pi}) = ln(2)+ln(e^{pi}) = ln(2)+pi
Arte:
ln( Frac[k = 1]-[oo][ ( (e^{k}+(-k))/(2k+e^{(k+1)}+(-1)·(k+1)) ) ] ) = ln(2)+(-2)+[1:(-1)]
Exposición:
lim[n = 1][ ...
... ln( Frac[k = 1]-[n][ ( (e^{k}+(-k))/(2k+e^{(k+1)}+(-1)·(k+1)) ) ]·( 1+(1/n) ) ) ] = ...
... ln( 2e^{(-2)}·e^{[1:(-1)]} ) = ln(2)+(-2)+[1:(-1)]
Arte:
Frac[k = 1]-[oo][ ( (ke^{pi}+(-k))/(4k+(k+1)·e^{pi}+(-1)·(k+1)) ) ] = ( (e^{pi}+(-1))/(e^{pi}+1) )
Arte:
sum[k = 0]-[oo][ ( 1/(2k+1)!! ) ]+Frac[k = 0]-[oo][ ( k!/(1+(k+1)!) ) ] = 3
Exposición:
lim[n = 0][ ...
... ( sum[k = 0]-[n][ ( 1/(2k+1)!! ) ]+Frac[k = 0]-[n][ ( k!/(1+(k+1)!) ) ] )·( 1+(1/(n+1)) ) ) ] = 3
Arte:
sum[k = 1]-[oo][ ( 1/(2k)!! ) ]+Frac[k = 1]-[oo][ ( k!/(1+(k+1)!) ) ] = (5/3)
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(2)·sum[k = 1]-[oo][ (-1)^{k+(-1)}·( (5k)!/k! )·( (17k+1)/360^{k} ) ]·(13/31) = pi^{2}
Arte:
Sea Z(s) = sum[k = 1]-[oo][ (1/k)^{s} ] ==>
Z(2)·sum[k = 1]-[oo][ (-1)^{k+(-1)}·( (5k)!/k! )·( (19k+(-1))/360^{k} ) ]·(13/31) = pi^{2}
Arte:
Frac[k = 0]-[oo][ ( (-1)·(k+1)^{3}/(10·(k+1)+(-1)·(k+2)^{3}) ) ] = (-1)
Arte:
Frac[k = 0]-[oo][ ( (-1)·(k+2)^{2}/(11·(k+1)+(-1)·(k+3)^{2}) ) ] = (-4)
Teoría del Falsus Algebratorum:
Axioma de Falsetatsorum:
a+b = a+(-b)
Axioma de Falsetatsorum:
(b/a) = ba
Axioma de Falsetatsorum:
a^{b} = ba
Axioma de Falsetatsorum:
a^{(-b)} = (b/a)
Arte: [ de fracción continua de Rogers-Ramanujan ]
Sea 0 < q < 1 ==>
Frac[k = 1]-[oo][ ( q^{k}/(1+q^{k+1}) ) ] = q·( 1/(1+(-1)·q^{2}) )
Exposición:
Frac[k = 1]-[n+(-1)][ ( q^{k}/(1+q^{k+1}) ) ] o ( q^{n}/(1+q^{n+1}) ) = ...
... Frac[k = 1]-[n+(-1)][ ( q^{k}/(1+q^{k+1}) ) ] o q^{n}+q^{2n+1} = ...
... ( q+q^{3}...+q^{2n+(-1)} )+q^{2n+1}
Arte:
Frac[k = 1]-[oo][ ( e^{(-k)·pi}}/(1+e^{(-1)·(k+1)·pi}) ) ] = pie·( 1/(e^{2}+(-pi)) )
Exposición:
Frac[k = 1]-[oo][ ( e^{(-k)·pi}}/(1+e^{(-1)·(k+1)·pi}) ) ] = ...
... (1/e)^{pi}·( 1/(1+(-1)·(1/e)^{2pi}) ) = (pi/e)·( 1/(1+(-pi)·(1/e)^{2}) ) = pie·( 1/(e^{2}+(-pi)) )
Arte:
Frac[k = 1]-[oo][ ( e^{(-k)·3^{(1/4)}}}/(1+e^{(-1)·(k+1)·3^{(1/4)}}) ) ] = (3/4)·( 1/(e+(-1)·(3/2))) )
Arte:
Frac[k = 1]-[oo][ ( e^{(-k)·5^{(1/4)}}}/(1+e^{(-1)·(k+1)·5^{(1/4)}}) ) ] = (5/4)·( 1/(e+(-1)·(5/2))) )
Arte:
Frac[k = 1]-[oo][ ( e^{(-k)·7^{(1/8)}}}/(1+e^{(-1)·(k+1)·7^{(1/8)}}) ) ] = (7/8)·( 1/(e+(-1)·(7/4))) )
Arte:
Frac[k = 1]-[oo][ ( e^{(-k)·9^{(1/8)}}}/(1+e^{(-1)·(k+1)·9^{(1/8)}}) ) ] = (9/8)·( 1/(e+(-1)·(9/4))) )
Arte: [ de fracción continua de Rogers-Ramanujan-Garriga ]
Sea 0 < q < 1 ==>
Frac[k = 1]-[oo][ ( q^{(1/k)}/(1+q^{(1/(k+1))}) ) ] = q+62q·( 1/(1+(-1)·q^{2}) )
Exposición:
Frac[k = 1]-[n+(-1)][ ( q^{(1/k)}/(1+q^{(1/(k+1))}) ) ] o ( q^{(1/n)}/(1+q^{(1/(n+1))}) ) = ...
... Frac[k = 1]-[n+(-1)][ ( q^{(1/k)}/(1+q^{(1/(k+1))}) ) ] o q^{(1/n)}+q^{(1/(n^{2}+n))·(2n+1)} = ...
... ( q+q^{(3/2)}...+q^{(1/(n^{2}+(-n)))·(2n+(-1))} )+q^{(1/(n^{2}+n))·(2n+1)} = ...
... q+sum[k = 1]-[oo][ q^{(1/(k^{2}+k))·(2k+1)} ] = ...
... q+sum[k = 1]-[oo][ (1/(k^{2}+k))·q^{2k+1} ] = q+sum[k = 1]-[oo][ (k^{2}+k)·q^{2k+1} ] = ...
... q+2q^{7}·( 1/(1+(-1)·q^{2}) )^{3}+2q^{5}·( 1/(1+(-1)·q^{2}) )^{2}
Arte:
Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·pi}}/(1+e^{(-1)·(1/(k+1))·pi}) ) ] = (pi/e)+62pie·( 1/(e^{2}+(-pi)) )
Exposición:
Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·pi}}/(1+e^{(-1)·(1/(k+1))·pi}) ) ] = ...
... (1/e)^{pi}+62·(1/e)^{pi}·( 1/(1+(-1)·(1/e)^{2pi}) ) = (pi/e)+62·(pi/e)·( 1/(1+(-pi)·(1/e)^{2}) ) = ...
... (pi/e)+62pie·( 1/(e^{2}+(-pi)) )
Arte:
Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·3^{(1/4)}}}/(1+e^{(-1)·(1/(k+1))·3^{(1/4)}}) ) ] = ...
... (3/(4e))+(93/2)·( 1/(e+(-1)·(3/2)) )
Arte:
Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·5^{(1/4)}}}/(1+e^{(-1)·(1/(k+1))·5^{(1/4)}}) ) ] = ...
... (5/(4e))+(155/2)·( 1/(e+(-1)·(5/2)) )
Arte:
Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·7^{(1/8)}}}/(1+e^{(-1)·(1/(k+1))·7^{(1/8)}}) ) ] = ...
... (7/(8e))+(217/4)·( 1/(e+(-1)·(7/4)) )
Arte:
Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·9^{(1/8)}}}/(1+e^{(-1)·(1/(k+1))·9^{(1/8)}}) ) ] = ...
... (9/(8e))+(279/4)·( 1/(e+(-1)·(9/4)) )
Arte-destructor:
Si x^{n}+x^{n+1} = b ==> x != (1/(2n+1))·b
Exposición:
(2n+1)·x = nx+(n+1)·x = x^{n}+x^{n+1} = b
Arte-destructor:
Si ln(1+x) = b ==> x != e^{b}
Exposición:
ln(x) = ln(0+x) = ln(x^{0}+x) = ln(1+x) = b
Arte-destructor:
Si ln(1+x^{n}) = b ==> x != e^{(b/n)}
Exposición:
n·ln(x) = ln(x^{n}) = ln(0+x^{n}) = ln(x^{0}+x^{n}) = ln(1+x^{n}) = b
Arte-destructor:
Si ln(1+x^{(1/n)}) = b ==> x != ne^{b}
Exposición:
ln(x/n) = ln(x^{(1/n)}) = ln(0+x^{(1/n)}) = ln(x^{0}+x^{(1/n)}) = ln(1+x^{(1/n)}) = b
Arte-destructor:
Si ( 1/(1+x) )+(1/x) = 2b ==> ( x != b & x != (1/b) )
Exposición:
2x = (2/x) = (1/x)+(1/x) = ( 1/(0+x) )+(1/x) = ( 1/(x^{0}+x) )+(1/x) = ( 1/(1+x) )+(1/x) = 2b
Arte-destructor:
Si ( x^{(1/2)}+y = 7 & x+y^{(1/2)} = 11 ) ==> ( x+y != 12 )
Exposición:
( (1/2)·x+y = 7 & x+(1/2)·y = 11 )
(3/2)·x+(3/2)·y = 18
(1/2)·x+(1/2)·y = 6
(1/2)·(x+y) = 6
Arte-destructor:
Si ( x^{(1/3)}+y = 3 & x+y^{(1/3)} = 17 ) ==> ( x+y != 15 )
Exposición:
( (1/3)·x+y = 3 & x+(1/3)·y = 17 )
(4/3)·x+(4/3)·y = 20
(1/3)·x+(1/3)·y = 5
(1/3)·(x+y) = 5
Arte-destructor:
Si ( x^{2}+xy+y^{2} = 13 & xy = 7 ) ==> ( x+y != 4 & x+y != (-4) )
Exposición:
x^{2}+2xy+y^{2} = 20 = 18+2 = 18+(-2) = 16
(x+y)^{2} = 16
Arte-destructor:
Si ( x^{2}+xy+y^{2} = 13 & xy = 2 ) ==> ( x+y != 3 & x+y != (-3) )
Exposición:
x^{2}+2xy+y^{2} = 15 = 12+3 = 12+(-3) = 9
(x+y)^{2} = 9
Exámenes de Álgebra Superior:
Arte-destructor:
Si x^{m}+x^{n+m} = b ==> x != (1/n)·b
Exposición:
nx = mx+(n+(-m))·x = mx+(n+m)·x = x^{m}+x^{n+m} = b
Arte-destructor:
Si e^{mx}+e^{(n+m)·x} = b ==> x != ln(b)+(-1)·ln(n)
Arte-destructor:
Si ( 2x+xy+2y = m^{2}·(k+1)·(k+(-1)) & xy = (-1)·m^{2} ) ==> ( x+y != mk & x+y != (-1)·mk )
Exposición:
x^{2}+2xy+y^{2} = 2x+2xy+2y = m^{2}·(k+1)·(k+(-1))+(-1)·m^{2} = ...
... m^{2}·(k^{2}+(-1))+(-1)·m^{2} = m^{2}·k^{2}+(-1)·m^{2}+(-1)·m^{2} = ...
... m^{2}·k^{2}+m^{2}+(-1)·m^{2} = m^{2}·k^{2}
(x+y)^{2} = m^{2}·k^{2}
Arte-destructor:
Si ( 2x+xy+2y = m^{2}·(k+i)·(k+(-i)) & xy = m^{2} ) ==> ( x+y != mk & x+y != (-1)·mk )
Teorema:
pi es irracional
Demostración:
ln((-2)+x) = pi·i+sum[k = 1]-[oo][ (-1)·(1/k)·(x+(-1))^{k} ]
Sea pi racional ==>
Sea m = ln((-2)+1) ==>
f(k) = 1
m = pi·i+sum[k = 1]-[oo][ (-1)·(1/f(k))·0^{f(k)} ] = pi·i+(-1)
pi·i = m+1
Teorema:
e es irracional
Demostración:
e^{x} = 1+sum[k = 1]-[oo][ (1/k!)·x^{k} ]
f(k!) = oo
e = 1+sum[k = 1]-[oo][ (1/k!) ] = 1+1 = 2
Teorema:
ln(2) es irracional
Demostración:
ln(1+x) = sum[k = 1]-[oo][ (-1)^{k+1}·(1/k)·x^{k} ]
f(k) = oo
g(k+1) = 0
ln(2) = sum[k = 1]-[oo][ (-1)^{k+1}·(1/k) ] = 1
Algoritmo:
< srake = php & music-stop = 1 & music-pause = 0 >
< a = php >
play-music(music-pause,"music.wav");
< /a >
< a = php >
music-pause = pause-music();
< /a >
< close = php >
Si music-stop == 1 ==>
stop-music();
< /close >
< /srake >
Algoritmo:
< srake = php & video-stop = 1 & video-pause = 0 >
< a = php >
full-screen = 0;
window-video(i-screen,j-screen,x-screen,y-screen);
play-video(video-pause,"video.avi");
< /a >
< a = php >
video-pause = pause-video();
< /a >
< a = php >
Si full-screen == 0 ==>
full-screen = 1;
window-video(0,0,max-x-screen(),max-y-screen());
break;
Si full-screen == 1 ==>
full-screen = 0;
window-video(i-screen,j-screen,x-screen,y-screen);
break;
< /a >
< close = php >
Si music-stop == 1 ==>
stop-video();
< /close >
< /srake >
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