Bruno Marchal skrev:
A way to prove the consistency of a theory is to make a "visualization" of the theory. If you can visualize all that happens in the theory, then you know the theory is consistent. To visualize the natural numbers, you can think of them as a long sequence {0,1,2,3,4,5,...}, and this sequence is going far, far, away. But you can only visualize finite sequences. So you can think that you have a finite sequence of numbers, and you have a big black cloud far, far, away. You see the first part of the sequence {0,1,2,...,m} before the cloud. But inside the cloud you can imagine that you have the finite sequence {m+1,m+2,...,4*m-1,4*m}. This whole sequence {0,1,2,...,m,m+1,...4*m} is what you call the set N of all natural numbers. >From that set N you construct the true subset {0,2,4,6,...,2*m,2*m+2,...,4*m}, which you call the set E of all even numbers. The visible part of the set E is then {0,2,4,...,2*m}, and the hidden part of that sequence is {2*m+2,...,4*m}. Now you define a new concept INNFINITE, that is defined by: If you have a bijection from all visible numbers of a set S, to all visible numbers of a true subset of S, then you say that the set S in INNFINITE. Then you can use this concept INNFINITE, and you will get a consistent theory with no contradictions, because you have a finite visualization of this theory. -- Torgny --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~--- |

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