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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Thu, 10 Oct 2024 20:03:46 +0200
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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
>