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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Tue, 10 Dec 2024 07:19:05 -0500
Organization: i2pn2 (i2pn.org)
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On 12/9/24 9:40 AM, WM wrote:
> On 08.12.2024 21:22, joes wrote:
>> Am Tue, 03 Dec 2024 12:10:53 +0100 schrieb WM:
>>> On 03.12.2024 11:03, Mikko wrote:
>>>
>>>> I understand mathematics
>>> Hardly, though you may have the impression.
>>> Proof: You cannot understand that the function f(10n) = n from D = {10n
>>> | n ∈ ℕ} to ℕ = {1, 2, 3, ...} is not a bijection because for every
>>> initial segment {1, 2, 3, ..., n} of ℕ there are too few numbers of the
>>> form 10n that can be paired with numbers n.
>> Wow. For every segment there are numbers {10, 20, …, 10n}.
> 
> But for every segments more are needed: {1, 2, 3, ..., 10n}
> 
> Regards, WM
> 
> 
but {1, 2, 3, ..., 10n} would have its pairing with the set
{10, 20, 30, ... 100n}

The pairing is between TWO sets, not the members of a set with itself.