Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

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.

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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.