Re: Cantor's diagonal proof wrong?

From: Todd Trimble (trimble1_at_optonline.net)
Date: 11/15/04 

Date: Mon, 15 Nov 2004 20:11:04 +0000 (UTC)

On 15 Nov 2004, Anonymous wrote:
>You can certainly define the set of infinite integers to be the set of all
>integers plus all numbers that have an infinite progression of digits to the
>left of the decimal. This set, though, is larger than the set of integers
>since there is a 1 to 1 correspondence with the reals ... this set is not
>used much in standard mathematics either.

Guess it depends what you mean by "standard". There's a name
for this type of construction: working in base p, you are pointing
to so-called p-adic integers, which have been around for quite a
while, and which are a standard tool in number theory. But your
main point is right -- the set of p-adics is of the same cardinality
as the set of reals.

Todd Trimble