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

Am Thu, 10 Oct 2024 20:03:46 +0200 schrieb WM:

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!

You say w/2 were natural and comes after the darkness. What is the
smallest such number, w/w? And what is the biggest number that comes
before?

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.

WDYM "causes"? There is no such segment.
WDYM "inf. endsegments"? Inf. many of them or inf. sized ones?

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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.