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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Thu, 10 Oct 2024 23:07:36 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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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?

-- 
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.