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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?
Date: Wed, 9 Oct 2024 15:35:10 +0200
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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.
>>>>> What does „they” refer to in the last sentence?
>>>> All endsegments which have infinitely many natural numbers.
>>> 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.
> Such an intersection is itself part of the sequence.

Of course.
> 
>>> 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.

>> 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.
> 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.

Regards, WM


>