doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
"Beyond the matrix II" game
The fact that Y objects (objects of X bits each) are defines both in S and P(S), enables use to define a bijection between N and P(N) objects, by simply defining a mapping between each natural number and each different case of some inverse object of the diagonal of that particular X^2 matrix.
Furthermore, S < 2^S is false, where |S| is finite or not, because it is clearly shown that there is a bijection between each natural number and each given case of different inverse object of the diagonal of some S with different X^2 matrix's arrangement.
Actually, there is S ↔ ...P(P(S))... and since the cardinality of the collection of all ...P(P(S))... is unsatisfied, then the cardinality of S is unsatisfied (incomplete).
Here is an example (based on "Beyond the matrix II" game http://www.internationalskeptics.com/forums/showpost.php?p=6907490&postcount=14351 ):
Here is some collection of P({apple, orange, lemon}) different objects, that were translated to <0,1>^|{apple, orange, lemon}| different objects:
{
000 ↔ {}
001 ↔ {apple}
010 ↔ {orange}
011 ↔ {lemon}
100 ↔ {apple,orange}
101 ↔ {apple,lemon}
110 ↔ {orange,lemon}
111 ↔ {apple, orange, lemon}
}
As can be seen the generalized <0,1>^3 forms have the same structural principle, whether they are used as P(X) or X objects, for example:
P(X)=
{
000,
001,
010,
011,
100,
101,
110,
111
}
X=
(
{
100,
110,
111
} → 000 not in the range of this particular arrangement of different <0,1> forms (where each particular arrangement is X^2 of <0,1> bits)
or
{
101,
010,
000
} → 001 not in the range of this particular arrangement of different <0,1> forms (where each particular arrangement is X^2 of <0,1> bits)
Etc…
)
Our mapping is done between each natural number and each inverse of the diagonal of each particular arrangement is X^2 of <0,1> bits, as follows:
1 ↔ 000
2 ↔ 001
...
etc. and it is shown that there is a bijection between natural numbers and any different object of 2^S collection.
Furthermore, since the diagonal method is invariant for ...2^(2^(2^S)))..., whether |S| is finite or not, there is a bijection between natural numbers and the inverse of the diagonals of ...2^(2^(2^S)))... and since the cardinality of the collection of all ....2^(2^(2^S)))... is unsatisfied, then the cardinality of natural numbers is unsatisfied (incomplete).
----------------
The same principle is shown by using Cantor's theorem ( http://en.wikipedia.org/wiki/Cantor's_theorem ).
By this theorem, cantors explicitly provides a 2^N object, called D, that is not in the range of N objects. But as we have shown above, if the bijunction is done by using such an explicitly provided 2^N object (D object) and some natural number, then there is a bijection between each natural number and each 2^N D object, where Cantor's theorem is some single case that provides an explicit 2^N D object that can be put in one-to-one correspondence with some distinct natural number.
Again, Cantor's theorem is actually a consistent method to provide some explicit 2^N D object that can be put be put in one-to-one correspondence with some distinct natural number.
Cantor's mistake is based on the fact that he concluded general conclusions by using only a one round of his theorem.
And he did it by using at least a collection of different <0,1> forms, which according to it, there are <0,1> forms with the same number of bits (what you call Y objects) both in S AND 2^S, such that the inverse of the diagonal of some particular S different objects' arrangment (which is actually a X^2 <0,1> matrix, where the number of bits of each different object, and the number of objects, have the same cardinality) is also an object of X bits, even if the considered collection is P(S) or 2^S (where the number of different <0,1> forms is greater than the number of the bits of each form).
The fact that Y objects (objects of X bits each) are defines both in S and P(S), enables use to define a bijection between N and P(N) objects, by simply defining a mapping between each natural number and each different case of some inverse object of the diagonal of that particular X^2 matrix.
Furthermore, S < 2^S is false, where |S| is finite or not, because it is clearly shown that there is a bijection between each natural number and each given case of different inverse object of the diagonal of some S with different X^2 matrix's arrangement.
Actually, there is S ↔ ...P(P(S))... and since the cardinality of the collection of all ...P(P(S))... is unsatisfied, then the cardinality of S is unsatisfied (incomplete).
It can't, because its cardinality is unsatisfied.
Here is an example (based on "Beyond the matrix II" game http://www.internationalskeptics.com/forums/showpost.php?p=6907490&postcount=14351 ):
Here is some collection of P({apple, orange, lemon}) different objects, that were translated to <0,1>^|{apple, orange, lemon}| different objects:
{
000 ↔ {}
001 ↔ {apple}
010 ↔ {orange}
011 ↔ {lemon}
100 ↔ {apple,orange}
101 ↔ {apple,lemon}
110 ↔ {orange,lemon}
111 ↔ {apple, orange, lemon}
}
As can be seen the generalized <0,1>^3 forms have the same structural principle, whether they are used as P(X) or X objects, for example:
P(X)=
{
000,
001,
010,
011,
100,
101,
110,
111
}
X=
(
{
100,
110,
111
} → 000 not in the range of this particular arrangement of different <0,1> forms (where each particular arrangement is X^2 of <0,1> bits)
or
{
101,
010,
000
} → 001 not in the range of this particular arrangement of different <0,1> forms (where each particular arrangement is X^2 of <0,1> bits)
Etc…
)
Our mapping is done between each natural number and each inverse of the diagonal of each particular arrangement is X^2 of <0,1> bits, as follows:
1 ↔ 000
2 ↔ 001
...
etc. and it is shown that there is a bijection between natural numbers and any different object of 2^S collection.
Furthermore, since the diagonal method is invariant for ...2^(2^(2^S)))..., whether |S| is finite or not, there is a bijection between natural numbers and the inverse of the diagonals of ...2^(2^(2^S)))... and since the cardinality of the collection of all ....2^(2^(2^S)))... is unsatisfied, then the cardinality of natural numbers is unsatisfied (incomplete).
----------------
The same principle is shown by using Cantor's theorem ( http://en.wikipedia.org/wiki/Cantor's_theorem ).
By this theorem, cantors explicitly provides a 2^N object, called D, that is not in the range of N objects. But as we have shown above, if the bijunction is done by using such an explicitly provided 2^N object (D object) and some natural number, then there is a bijection between each natural number and each 2^N D object, where Cantor's theorem is some single case that provides an explicit 2^N D object that can be put in one-to-one correspondence with some distinct natural number.
Again, Cantor's theorem is actually a consistent method to provide some explicit 2^N D object that can be put be put in one-to-one correspondence with some distinct natural number.
Cantor's mistake is based on the fact that he concluded general conclusions by using only a one round of his theorem.
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