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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Wed, 9 Oct 2024 17:08:02 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Wed, 09 Oct 2024 14:48:17 +0200 schrieb WM:
> On 08.10.2024 23:08, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>> On 07.10.2024 18:11, Alan Mackenzie wrote:
>>>> What I should have written (WM please take note) is:
>> 
>>>> The idea of one countably infinite set being "bigger" than another
>>>> countably infinite set is simply nonsense.
>>> The idea is supported by the fact that set A as a superset of set B is
>>> bigger than B.
>> What do you mean by "bigger" as applied to two infinite sets when one
>> of them is not a subset of the other?
> That is not in every case defined. But here are some rules:
> Not all infinite sets can be compared by size, but we can establish some
> useful rules.
[copypasta]
That is a weakness of your notion of cardinality.
How do you compare finite sets?

>>> Simply nonsense is the claim that there are as many algebraic numbers
>>> as prime numbers.
>> It is not nonsense.  The prime numbers can be put into 1-1
>> correspondence with the algebraic numbers, therefore there are exactly
>> as many of each.
> Nonsense. Only potential infinity is used. Never the main body is
> applied.
What "main body"?

>>> For Cantor's enumeration of all fractions I have given a simple
>>> disproof.
>> Your "proofs" tend to be nonsense.
> Theorem: If every endsegment has infinitely many numbers, then
> infinitely many numbers are in all endsegments.
> Proof: If not, then there would be at least one endsegment with less
> numbers.
I struggle to follow this illogic. Why should one segment have less 
numbers?

> Note: The shrinking endsegments cannot acquire new numbers.
Not necessary, they already contain as many as needed. 

-- 
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.