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

On 19.10.2024 17:27, joes wrote:

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

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.

No. But the density of the numbers is halved.
 > "Doubling" is a total function: every natural is
 > mapped to exactly one other.
But not to one of the original set.

 

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.

If every natural is mapped to exactly one other, then half of them are not elements of the mapped set. The set ha grown.
Regards, WM