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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: Wed, 9 Oct 2024 12:26:04 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <a01d39f9ddfffb6d2aa104fe49476cd11f492f29@i2pn2.org>
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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.

>> What we are talking about is the, pardon,
>> limit of whatever function.
> The limit-endsegment is empty.
Why?

>> Shouldn’t the limit of 1/n be 1/ω != 0 ?

>>>> There is no natural number which has no successors.
>>> Infinite endsegments contain infinitely many numbers and therefore an
>>> infinite intersection.
>> Can you explain to me what an infinite intersection is?
> 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?

-- 
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.