destructor matemático

teorema constructor:

x < y <==> z+x < z+y

x < y

z+x < z+y

(-z)+z+x < (-z)+z+y

(-0)+x < (-0)+y

x < y

teorema destructor

x < y <==> z+y [< z+x

x < y

¬( z+x < z+y )

z+y [< z+x

teorema constructor:

x [< y <==> z+x [< z+y

x [< y

z+x [< z+y

(-z)+z+x [< (-z)+z+y

(-0)+x [< (-0)+y

x [< y

teorema destructor

x [< y <==> z+y < z+x

x [< y

¬( z+x [< z+y )

z+y < z+x

teorema constructor:

x > y <==> z+x > z+y

x > y

z+x > z+y

(-z)+z+x > (-z)+z+y

(-0)+x > (-0)+y

x > y

teorema destructor

x > y <==> z+y >] z+x

x > y

¬( z+x > z+y )

z+y >] z+x

teorema constructor:

x >] y <==> z+x >] z+y

x >] y

z+x >] z+y

(-z)+z+x >] (-z)+z+y

(-0)+x >] (-0)+y

x >] y

teorema destructor

x >] y <==> z+y > z+x

x >] y

¬( z+x >] z+y )

z+y > z+x

teorema constructor:

x < y <==> x+z < y+z

x < y

x+z < y+z

x+z+(-z) < y+z+(-z)

x+0 < y+0

x < y

teorema destructor

x < y <==> y+z [< x+z

x < y

¬( x+z < y+z )

y+z [< x+z

teorema constructor:

x [< y <==> x+z [< y+z

x [< y

x+z [< y+z

x+z+(-z) [< y+z+(-z)

x+0 [< y+0

x [< y

teorema destructor

x [< y <==> y+z < x+z

x [< y

¬( x+z [< y+z )

y+z < x+z

teorema constructor:

x > y <==> x+z > y+z

x > y

x+z > y+z

x+z+(-z) > y+z+(-z)

x+0 > y+0

x > y

teorema destructor

x > y <==> y+z >] x+z

x > y

¬( x+z > y+z )

y+z >] x+z

teorema constructor:

x >] y <==> x+z >] y+z

x >] y

x+z >] y+z

x+z+(-z) >] y+z+(-z)

x+0 >] y+0

x >] y

teorema destructor

x >] y <==> y+z > x+z

x >] y

¬( x+z >] y+z )

y+z > x+z

teorema constructor:

Si ( ( 0 < x & 0 < y ) || ( x < (-0) & y < (-0) ) ) ==> 0 < x·y

( 0 < x & 0 < y ) || ( x < (-0) & y < (-0) )

( 0 < x & 0 < y ) || ( 0 < (-x) & 0 < (-y) )

( 0·y < x·y & x·0 < x·y ) || ( 0·(-y) < (-x)·(-y) & (-x)·0 < (-x)·(-y) )

( 0 < x·y & 0 < x·y ) || ( 0 < (-x)·(-y) & 0 < (-x)·(-y) )

0 < x·y || 0 < (-x)·(-y)

0 < (1·1)·x·y || 0 < ((-1)·(-1))·x·y

0 < 1·x·y || 0 < 1·x·y

0 < x·y || 0 < x·y

0 < x·y

teorema destructor

Si ( ( 0 < x & 0 < y ) || ( x < (-0) & y < (-0) ) ) ==> x·y [< 0

¬( 0 < x·y )

x·y [< 0

Moisés y Ramsés

Moisés Akenatón,

reformador judío.

Sin tumba.

Se ha vado de la Tierra.

Sus estatuas no son humanas,

porque Moisés, no está en la Tierra.

Moisés fue tratado bien,

por su hermano menor Ramsés,

cuando Ramsés fue faraón.

Ramsés Tutankamón,

anti-reformador judío.

Con tumba.

No se ha vado de la Tierra.

Sus estatuas son humanas,

porque Ramsés, está en la Tierra.

Ramsés fue tratado bien,

por su hermano mayor Moisés,

cuando Moisés fue faraón.

lógica borrosa

¬a = 1+(-a)

¬¬a = 1+( (-1)+a ) = a

¬a = ln((1+e)+(-1)·e^{a})

¬¬a = ln((1+e)+(-1)·e^{ln((1+e)+(-1)·e^{a})}) = ln((1+e)+(-1)·(1+e)+e^{a}) = ln(e^{a}) = a

¬a = ( 1+(-1)·a^{(1/n)} )^{n}

¬¬a = ( 1+(-1)·( 1+(-1)·a^{(1/n)} ) )^{n} = a

¬a = ( 1+(-1)·a^{n} )^{(1/n)}

¬¬a = ( 1+(-1)·( 1+(-1)·a^{n} ) )^{(1/n)} = a

destructor matemático

Aprended destructor matemático que neutraliza el constructor matemático,

y matan los símbolos de condenación a los dioses del mal.

Para que te jodan los esclavos infieles de un dios,

te tiene que vencer el destructor con constructor.

totalmente ordenado: ( x [< y || x >] y )

teorema constructor:

Si ( x < y & y < z ) ==> x < z

x < y < z

x < z

teorema destructor:

Si ( x < y & y < z ) ==> z [< x

¬( x < z )

z [< x

teorema constructor:

Si ( x [< y & y [< z ) ==> x [< z

x [< y [< z

x [< z

teorema destructor:

Si ( x [< y & y [< z ) ==> z < x

¬( x [< z )

z < x

teorema constructor:

Si ( x > y & y > z ) ==> x > z

x > y > z

x > z

teorema destructor:

Si ( x > y & y > z ) ==> z >] x

¬( x > z )

z >] x

teorema constructor:

Si ( x >] y & y >] z ) ==> x >] z

x >] y >] z

x >] z

teorema destructor:

Si ( x >] y & y >] z ) ==> z > x

¬( x >] z )

z > x

teorema constructor:

Si ( x [< y & y < z ) ==> x < z

( x < y || x = y ) & y < z

x < z || x < z

x < z

teorema destructor:

Si ( x [< y & y < z ) ==> z [< x

¬( x < z )

z [< x

teorema constructor:

Si ( x < y & y [< z ) ==> x < z

x < y & ( y < z || y = z )

x < z || x < z

x < z

teorema destructor:

Si ( x < y & y [< z ) ==> z [< x

¬( x < z )

z [< x

teorema constructor:

Si ( x >] y & y > z ) ==> x > z

( x > y || x = y ) & y > z

x > z || x > z

x > z

teorema destructor:

Si ( x >] y & y > z ) ==> z >] x

¬( x > z )

z >] x

teorema constructor:

Si ( x > y & y >] z ) ==> x > z

x > y & ( y > z || y = z )

x > z || x > z

x > z

teorema destructor:

Si ( x > y & y >] z ) ==> z >] x

¬( x > z )

z >] x

Si ( A [<< B & B [<< C ) ==> A [ \ ] C != 0

¬( A [<< C )

¬[Ax][ x€A ==> x€C ]

[Ex][ x€A & ¬( x€C ) ]

[Ex][ x€ A [ \ ] C ]

A [ \ ] C != 0 [ [Ax][ ¬( x€A ) ] <==> A = 0 ]

Si ( A >>] B & B >>] C ) ==> A [ / ] C != 0

¬( A >>] C )

¬[Ax][ x€A <== x€C ]

[Ex][ ¬( x€A ) & x€C ]

[Ex][ x€ A [ / ] C ]

A [ / ] C != 0 [ [Ax][ ¬( x€A ) ] <==> A = 0 ]

teorema constructor:

A [ |o| ] B = 0 <==> A = B

A [ |o| ] B != 0

[Ex][ x€ A [ |o| ] B ]

[Ex][ x€ A |o| x€B ]

[Ex][ ¬( x€ A <==> x€B ) ]

¬[Ax][ x€ A <==> x€B ]

A != B

teorema destructor:

A [ |o| ] B != 0 <==> A = B

A [ |o| ] B != 0

[Ex][ x€ A [ |o| ] B ]

[Ex][ x€A |o| x€B ]

¬( ¬[Ax][ ¬( x€A |o| x€B ) ] )

[Ax][ ¬( x€A |o| x€B ) ]

[Ax][ x€A <==> x€B ]

A = B

teorema constructor:

A [ |o| ] B = 0 <==> A = B

A [ |o| ] B = 0

[Ax][ ¬( x€ A [ |o| ] B ) ]

[Ax][ ¬( x€ A |o| x€B ) ]

[Ax][ x€ A <==> x€B ]

A = B

teorema destructor:

A [ |o| ] B = 0 <==> A != B

A [ |o| ] B = 0

[Ax][ ¬( x€ A [ |o| ] B ) ]

¬( ¬[Ex][ x€A [ |o| ] B ] )

[Ex][ x€A |o| x€B ] )

¬¬[Ex][ x€A |o| x€B ]

¬[Ax][ ¬( x€A |o| x€B ) ]

¬[Ax][ x€A <==> x€B ]

A != B

límits

lim[x-->a][ (f(x)/x) ] = 1 <==> lim[x-->a][ f(x) ] = a

lim[x-->a][ (f(x)/(-x)) ] = 1 <==> lim[x-->a][ f(x) ] = (-a)

lim[x-->a][ (f(x)·x) ] = 1 <==> lim[x-->a][ f(x) ] = (1/a)

lim[x-->a][ (f(x)·(-x)) ] = 1 <==> lim[x-->a][ f(x) ] = (1/(-a))

x·(1/x) = 1

0·(1/0) = 1 = 0·oo

x^{n}·(1/x^{n}) = 1

0^{n}·(1/0^{n}) = 1 = 0^{n}·oo^{n}

0^{n} < 0 <==> oo < oo^{n}

(-0) < (-1)·0^{n}  <==> (-1)·oo^{n} < (-1)·oo

(-0) < ...< (-1)·0^{n} < 0^{n} < ...< 0 <==> (-1)·oo^{n} < ...< (-1)·oo < oo < ...< oo^{n}

lim[ n ] = oo

lim[ (1/n) ] = 0

(n/m)·oo+1 = (n/m)·oo

1+(m/n)·0 = 1

lim[ (n^{p}+an^{p+1})/(n^{p}+bn^{p+1}) ] = ...

... lim[ (n^{p+1}/n^{p+1})·((1/n)+a)/((1/n)+b) ] = (a/b)

lim[ (n^{p}+an^{p+1})/(n^{p}+bn^{p+1}) ] = ...

... lim[ (n^{p}/n^{p})·(1+an)/(1+bn) ] = (a/b)

(n/m)·oo^{(n+1)}+oo^{n} = (n/m)·oo^{(n+1)}

0^{n}+(m/n)·0^{(n+1)} = 0^{n}

lim[ (2n)/(n+2n^{2}+3n^{3}+4n^{4}) ] = (1/2)·0^{3}

lim[ (2n+4n^{2})/(n+2n^{2}+3n^{3}+4n^{4}) ] = 0^{2}

lim[ (2n+4n^{2}+8n^{3})/(n+2n^{2}+3n^{3}+4n^{4}) ] = 2·0

lim[ (2n+4n^{2}+8n^{3}+16n^{4})/(n+2n^{2}+3n^{3}+4n^{4}) ] = 4

lim[ (1+(1/n))^{n} ] = e

d_{x}[ln(x)] = lim[h-->0][ (1/x)·ln( (1+(h/x) )^{x/h}) = (1/x)

lim[h-->0][ ( 1+(h/x) )^{x/h} ] = e

lim[ ( 1+( (kn+1)/(n^{2}+1) ) )^{n} ] = ...

... lim[ ( ( 1+( (kn+1)/(n^{2}+1) )^{(n^{2}+1)/(kn+1)} )^{( ( n(kn+1) )/(n^{2}+1) )} ] = e^{k}

x+(-x) = 0

(-x)+x = (-0)

0^{n}+(-1)·0^{n} = 0^{(n+1)}

(-1)·0^{n}+0^{n} = (-1)·0^{(n+1)}

oo^{(n+1)}+(-1)·oo^{(n+1)} = oo^{n}

(-1)·oo^{(n+1)}+oo^{(n+1)} = (-1)·oo^{n}

lim[ (n+1)^{m}+(-1)·n^{m} ] = ( m+1 )·oo^{( m+(-1) )}

lim[ (1/(n+1)^{m})+(-1)·(1/n^{m}) ] = ( (-m)+1 )·oo^{( (-m)+(-1) )}

lim[ ( (1+...(n)...+n)/n ) ] = (oo/2)

Stolz:

lim[ (n+1)/((n+1)+(-1)·n) ] = (oo/2) [ oo+(-1)·oo = 1 ]

lim[ ( (1^{2}+...(n)...+n^{2})/n^{2} ) ] = (oo/3)

Stolz:

lim[ (n+1)^{2}/((n+1)^{2}+(-1)·n^{2}) ] = (oo/3) [ oo^{2}+(-1)·oo^{2} = oo ]

lim[ ( (1^{3}+...(n)...+n^{3})/n^{3} ) ] = (oo/4)

Stolz:

lim[ (n+1)^{3}/((n+1)^{3}+(-1)·n^{3}) ] = (oo/4) [ oo^{3}+(-1)·oo^{3} = oo^{2} ]

Stolz:

Si lim[ a_{n+1} ] >] oo ==>

l+(-s) < a_{n+1}/(a_{n+1}+(-1)·a_{n}) < l+s

(a_{n+1}+(-1)·a_{1})·(l+(-s)) < a_{2}+...+a_{n+1} < (l+s)·(a_{n+1}+(-1)·a_{1})

l+(-s) < ( (a_{2}+...+a_{n+1})/a_{n+1} ) < l+s

l+(-s) < ( (a_{1}+...+a_{n})/a_{n} ) < l+s

lim[ ln(n!)/ln(n) ] = lim[ ( ln(n+1)/ln(1+(1/n)) ) ] = lim[ ln(n+1)·n ] = ln(oo^{oo})

lim[ (k+k^{2}+...+k^{n})/k^{n} ] = ...

... lim[ ( k^{(n+1)}/(k^{n+1}+(-1)·k^{n}) ) ] = ( k/(k+(-1)) )

lim[ (k+k^{(1/2)}+...+k^{(1/n)})/k^{(1/n)} ] = ...

... lim[ ( k^{( 1/(n+1) )}/(k^{( 1/(n+1) )}+(-1)·k^{(1/n)}) ) ] = ( 1/(1+(-1)) ) = oo

lim[ (1!+2!+...+n!)/n! ] = lim[ ( (n+1)!/((n+1)!+(-1)·n!) ) ] = ( (n+1)/n ) = 1

oo^{a_{1}}+...+oo^{a_{n}} = oo^{max{a_{1},...,a_{n}}}

0^{a_{1}}+...+0^{a_{n}} = 0^{min{a_{1},...,a_{n}}}

llaunes y contingut y preu

llauna <==> 2pi·rh

contingut <==> pi·r^{2}·h

(f(r)/pi) = p·2rh+(-n)·r^{2}·h

d_{r}[ (f(r)/pi) ] = p·2h+(-n)·2rh = 0

p = n·r

discos en un cuadrat y preu

2r·a = x

4r^{2}·a^{2} = x^{2}

f(r) = p·2r·a+(-n)·4r^{2}·a^{2}

d_{r}[f(r)] = p·2a+(-n)·8r·a^{2} = 0

p = 4r·a·n

a = 10 & n = (2€/10000(cm)^{2}) & r = 5cm ==> p·2r·a = 4€

f(5) = 4+(-2) = 2€

a = 20 & n = (1€/10000(cm)^{2}) & r = 2.5cm ==> p·2r·a = 2€

f(2.50) = 2+(-1) = 1€

 

preu de fàbrica: 4€ || 2€

10% de iva:

preu de tenda: 8.80€ || 4.40€

preu de tenda de societat limitada única: 13.20€ || 6.60€