Lley de medicació

no desearás, ni el bien, ni el mal, del prójimo;
porque el cuerpo le pertenece a él.
No es pot obligar a medicar.

química: constructors y destructors

deca-tetra-nitrur-de-carboni


-C=C-N-C=C=C=C-N-C=C-
4 destructores + 3 constructores = 1 destructor


dodeca-tetra-nitrur de carboni


=C-C=C-N-C=C=C=C-N-C=C-C=
4 destructores + 5 constructores = 1 constructor

química: constructors y destructors

octo-nitrur-de-carboni


-C=C-N-C≡C-N-C=C-
2 destructores + 1 constructor = 1 destructor


-N-N-C=N-N=C-N-N-
2 destructores + 1 constructor = 1 destructor


deca-nitrur-de-carboni


=C-C=C-N-C≡C-N-C=C-C=
2 destructores + 3 constructores = 1 constructor


-N-N-N-C=N-N=C-N-N-N-
2 destructores + 3 constructores = 1 constructor

micro-economia: geometría una caisha de costat quadrat

F(x,z) = 16·( p( 2x^{2}+4xz )+(-1)mx^{2}z )


d_{x}[F(x,z)] = p( 4x+4z )+(-1)(2m)xz
d_{z}[F(x,z)] = p( 4z )+(-1)mx^{2}


x = 0
z = 0


p=(m^{2}/16)


d_{x}[F(x,z)] = (m^{2}/4)( x+z )+(-1)(2m)xz
d_{z}[F(x,z)] = (m^{2}/4)( z )+(-1)mx^{2}


x=(m/4)
z=(m/4)

constructor matemàtic borrós dos daus

en dos daus:


p=q


1=1
2=2
3=3
4=4
5=5
6=6


p( p=q ) = (6/36) = (1/6)


p+q=2


1+1=2


P( p+q=2 ) = (1/36)


p+q=12


6+6=12


P( p+q=12 ) = (1/36)


p+q=3


1+2=3
2+1=3


P( p+q=3 ) = (2/36) = (1/18)


p+q=11


5+6=11
6+5=11


P( p+q=11 ) = (2/36) = (1/18)


p+q=4


1+3=4
2+2=4
3+1=4


P( p+q=4 ) = (3/36) = (1/12)


p+q=10


4+6=10
5+5=10
6+4=10


P( p+q=10 ) = (3/36) = (1/12)


p+q=5


1+4=5
2+3=5
3+2=5
4+1=5


P( p+q=5 ) = (4/36) = (1/9)


p+q=9


3+6=9
4+5=9
5+4=9
6+3=9


P( p+q=9 ) = (4/36) = (1/9)


p+q=6


1+5=6
2+4=6
3+3=6
4+2=6
5+1=6


P( p+q=6 ) = (5/36)


p+q=8


2+6=8
3+5=8
4+4=8
5+3=8
6+2=8


P( p+q=8 ) = (5/36)


p+q=7


1+6=7
2+5=7
3+4=7
4+3=7
5+2=7
6+1=7


P( p+q=7 ) = (6/36) = (1/6)

limits de successions

lim ( oo+(-n) ) = 0
( oo+(-oo) ) = 0


lim ( (oo+p)+(-n) ) = p
( (oo+p)+(-oo) ) = p


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


lim ( ( (oo+1)^{2}+(-1)(n^{2}+1) )/n ) = 2
( ( (oo+1)^{2}+(-1)(oo^{2}+1) )/oo ) = 2


lim ( ( (oo+1)^{2}+(-1)(n+(-1))^{2} )/n ) = 4
( ( (oo+1)^{2}+(-1)(oo+(-1))^{2} )/oo ) = 4


lim ( ( (oo+1)^{2}+(-1)(n+1) )/(n^{2}+n) ) = 1
( ( (oo+1)^{2}+(-1)(oo+1) )/(oo^{2}+oo) ) = 1


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


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

progressions aritmética, geométrica y potencial

( a_{1}=b & a_{n+1} = a_{n}+b ) <==> a_{n+1}=(n+1)·b


( a_{1}=b & a_{n+1} = b·a_{n} ) <==> a_{n+1}=b^{(n+1)}


( a_{1}=b & a_{n+1} = (a_{n})^{m} ) <==> a_{n+1}=b^{m^{n+1}}