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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?
Date: Thu, 10 Oct 2024 11:26:25 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Wed, 09 Oct 2024 15:35:10 +0200 schrieb WM:
> On 09.10.2024 14:26, joes wrote:
>> Am Wed, 09 Oct 2024 11:47:57 +0200 schrieb WM:
>>> On 08.10.2024 21:23, joes wrote:
>>>> Am Tue, 08 Oct 2024 17:30:19 +0200 schrieb WM:
>>>>> On 08.10.2024 15:26, joes wrote:
>>>>>> Am Tue, 08 Oct 2024 12:46:01 +0200 schrieb WM:
>>>>>
>>>>>>> Because infinitely many natural numbers are contained. This is
>>>>>>> true for all infinite sets of the function. Therefore they cannot
>>>>>>> have lost all numbers.
All endsegments are infinite.
>>>>>> What does „they” refer to in the last sentence?
>>>>> All endsegments which have infinitely many natural numbers.
There are no others.
>>>> We are, again, not talking about an element of the sequence, which
>>>> has a natural index, contains infinitely many successors and is
>>>> missing a finite number of predecessors.
>>> I am talking about such endsegments. Their intersection is infinite.
Which intersection?
>> Such an intersection is itself part of the sequence.
> Of course.
What about the intersection of all infinitely many segments?

>>>> What we are talking about is the, pardon, limit of whatever function.
>>> The limit-endsegment is empty.
>> Why?
> Because every n has become an index and then is lost.
It is impossible to use up an infinity.

>>> The intersection is infinite because all infinite endsegments contain
>>> the same infinite set. Some have lost more or less numbers but the
>>> core remains infinite in all infinite endsegments.
No. You seem to imagine them as finite but sharing a mysterious omega.
Instead, replace that with "..." and you got it.
>> And how many segments have been intersected?
> (Potentially in-)finitely many because the collection of indices is
> finite as long as an infinite set of numbers remains within the
> endsegments.
And what if we intersect infinitely many?

-- 
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.