Re: Cantor's "proof"

From: Keckman (keckman_at_welho.com)
Date: 09/22/04 

Date: Wed, 22 Sep 2004 23:54:24 +0300

On 22 Sep 2004 13:19:48 -0700, Daryl McCullough <daryl@atc-nycorp.com>
wrote:

> But there is a real number d that is not on *any* of the lists you
> construct.

Same way as there is an _natural_ number that is not on *any* list you
construct (of natural numbers).

Let suppose you have listed natural numbers:

1: 3
2: 7
3: 99
.
.

Now, in every step lets construct a number by adding them: 3+7+99+...This
number is bigger than any number previously in list (do i have to prove it
to you?). The situation is same as in Cantor's list - he construct a
decimal number in every step that has not yet been on list - but it could
be next or later. It will be different than *any* only if we can go the
list trough, but we can't. Or if we can, then we can go this list too:

1: 0,1000...
2: 0,2000...
.
.
999: 0,999000....

33333.... : 0,3333333333....

And the last row is the answer to other Cantorist who ask where is the
place for the 0,3333333....

There is even place for the pii/10:

3141592653589... : 0,3141592652589...

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