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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 9 Jan 2025 21:06:43 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Thu, 09 Jan 2025 10:38:44 +0100 schrieb WM:
> On 09.01.2025 00:45, joes wrote:
>> Am Wed, 08 Jan 2025 23:06:27 +0100 schrieb WM:
> 
>>> The set {1, 2, 3, ...} is smaller by one element than the set {0, 1,
>>> 2,
>>> 3, ...}. Proof: {0, 1, 2, 3, ...} \ {1, 2, 3, ...} = {0}. Cardinality
>>> cannot describe this difference because it covers only mappings of
>>> elements which have almost all elements as successors.
>> You can't talk about size without using |abs|.
> I can and I do. And everybody understands it in case of subsets. This
> proves, in this special case (and more is not required), that Cantor's
> size is only a qualitative measure, not a quantitative one.
You have not defined any other concept of "size". How do, say,
the sets of  4*k +-1  relate?

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.