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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Thu, 21 Nov 2024 00:08:24 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Wed, 20 Nov 2024 19:42:41 +0100 schrieb WM:
> On 20.11.2024 19:18, joes wrote:
>> Am Wed, 20 Nov 2024 13:04:04 +0100 schrieb WM:
> 
>>> Try to count to a natural number that has fewer successors than
>>> predecessors. Impossible.
>> Because there are no such numbers.
> All successors are natural numbers.
So?

> If all can be counted, then no successors remain.
All at once or every single one?
There are no successors "after" all of the other numbers.

>>> But set theory claims that all natural numbers can be counted to such
>>> that no successors remain.
>> et your quantifiers in order:
> That is a foolish excuse.
You have shown that you don't understand them.

>> every single natural number is very clearly finite;
> Every number that can be counted to is finite.
There are countably infinite numbers, but ok.

> But every number that can
> be counted to has more successors than predecessors.
Every number, period. There is no number without successors.

> Therefore not every number can be counted to.
Well, the ordinal numbers less than epsilon_0 are called countably
infinite.

>> the cardinal number corresponding to the set of all of them is
>> countably infinite.
> The  set of all numbers that can be counted to is finite, namely a
> number that is counted to. This cannot change by counting.
WTF there is no largest number. How do you think counting changes 
anything?

-- 
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.