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

Am Tue, 08 Oct 2024 17:26:43 +0200 schrieb WM:

On 08.10.2024 15:24, joes wrote:

Am Tue, 08 Oct 2024 12:51:03 +0200 schrieb WM:

On 07.10.2024 17:18, joes wrote:

Am Mon, 07 Oct 2024 11:08:33 +0200 schrieb WM:

On 07.10.2024 10:05, joes wrote:

Am Mon, 07 Oct 2024 09:41:23 +0200 schrieb WM:

On 06.10.2024 17:48, Alan Mackenzie wrote:
even an unbounded sequence does not get longer when shifted by one
step.

Nor does it get shorter, it stays infinite.

It keeps all its elements but not more.

„More” being a different kind of infinity, namely at least
uncountable.

Nonsense.

Only according to your broken concept of cardinality, by which N u {a}
is „bigger” than N, and N\{1} u {a} can’t even be compared.

Clearly they are the same „size”.

All ω+k are equally infinite.

Nonsense.

This is your useless replacement of cardinality.

Of course stopping after a finite number, which potential infinity
seems to mean, is not „complete” in that sense. Hilbert’s Hotel is
actually infinite, it already holds infinite guests.

Name them by all the natural numbers. Then no further guest can
appear.

It can, if I begin numbering with 2. The cardinality of N\{1} can’t
be finite.

Cardinality is nonsense.

Isn’t N\{1} finite? It has ω-1 elements.

But after the visble natural numbers the dark domain comes, and that is
what prevents to see the end (which is dark too).

But ω-1 is a finite natural.

That shows my point. Infinite sets can be moved. 0.999...999 moved
gives 9.99...9990.

You have not indicated what this notation means. Where does the zero
come from?

The last natural index has lost its 9 by shifting to the left-hand side.
Hence there is nothing remaining.

Moving a set does not remove elements. You cannot shift through the
darkness.

Another point is this: [0, 1) moved gives (0, 1].

Can you generalise this?

What example do you have in mind?

Any interval with both ends open/closed.

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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.