Re: Cantor and the binary tree



Ron Sperber wrote:

line number n
0 0.
1 0 1
2 0 1 0 1
... ..................

> It simply boggles my mind that this simple proof gives so many people
> such fits that they refuse to accept it. I continue to be sadly shocked
> by the number of posts on sci.math daily refuting Cantor's proof. Of
> course they are always fuzzy on details, but that's to be expected since
> they can't actually disprove it.

You are talking about Cantor's proof. You could say the same about
mine. I do not say, here, that Canor's proof is wrong. All I say, here,
is that another proof leads to another result. The reason is that set
theory is inconsistent. If you do not agree, then point out that step
of my proof, which is invalid.

1) Each real number of (0,1) is given by a path stretching over
infinitely many nodes (bits).
2) All nodes (bits) of the tree belong to a countable set.
3) A node can only exist within a path.
4) Any node increases the number of paths by 1, from 1 coming in to 2
going out. 2 - 1 = 1.
5) Any node increases the number of nodes by 1.

Regards, WM

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