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

On 09.10.2024 19:30, joes wrote:

Am Wed, 09 Oct 2024 16:40:21 +0200 schrieb WM:

When we *in actual infinity* multiply all |ℕ|natural numbers by 2,
then we keep |ℕ| numbers but only half of them are smaller than ω, i.e.,
are natural numbers. The other half is larger than ω.

So 2N = G u {w, w+2, w+4, ..., w+w-2}?

If all numbers are there initially and multiplied by 2. And if every number 2n is greater than n, then this is unavoidable.
Note the premise: If all are there. Actual infinity!

But what about the limit case, the intersection of all endsegments,
or the set which has lost an infinite number of elements?

The endsegment which has lost an infinite number of elements is empty and causes an empty intersection. But infinite endsegments have not lost an infinite number of numbers.
Regards, WM