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

Am Sat, 19 Oct 2024 15:18:56 +0200 schrieb WM:

On 19.10.2024 14:06, Moebius wrote:

Am 19.10.2024 um 13:21 schrieb joes:

Am Sat, 19 Oct 2024 11:24:54 +0200 schrieb WM:

On 18.10.2024 03:26, Richard Damon wrote:

 

It is proven that the set of Natural Numbers [is] closed under
multiplication.

That is not the set but the potentially infinite collection of Peano
numbers.

It is usually called N. Now the Mückenhirn unnaturals may not be closed
or infinite.

we are talking about THE SET OF NATURAL NUMBERS, IN,
and its elements -called NATURAL NUMBERS- here.
This set is infinite.

If we process all natural numbers and get more than we have processed,
then this is not a set but a collection, because sets do not change.

We don't get more. "Doubling" is a total function: every natural is
mapped to exactly one other.

Hint: Damit dieses "Reden" sinnvoll ist, bedarf es natürlich eines
entsprechenden mengentheoretischen Kontexts (->SET THEORY). (Das mag
viell. nicht jedem Gesprächsteilnehmer hier klar sein, ist aber so.)
 

[...] The set of natural numbers is infinite

and does not change --- neither shrink nor grow.

Why should it.

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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.