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

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.

Bijection is not about completeness, countability is.

Bijective means injective and surjective.

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.

All of them can at once move to the next
room,

All rooms are enumerated by all the natural numbers. Hence there is no chance to move. Only in potential infinity there is.
Regards, WM