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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Mon, 04 Nov 2024 06:08:01 -0500
Organization: Peripheral Visions
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Chris M. Thomasson explained on 11/4/2024 :
> On 11/3/2024 1:47 AM, FromTheRafters wrote:
>> joes submitted this idea :
>>> Am Sat, 02 Nov 2024 18:42:15 +0100 schrieb WM:
>>>> On 02.11.2024 14:50, Moebius wrote:
>>>>> Am 02.11.2024 um 14:21 schrieb joes:
>>>>>> Am Fri, 01 Nov 2024 18:03:26 +0100 schrieb WM:
>>>>>>> If an invariable set of numbers is there, then there is a smallest
>>>>>>> and a largest number of those which are existing.
>>>>> or each and every n e IN there is an n' e IN (say n' = n+1)
>>>> Actual infinity is not based on claims for each and every, but concerns
>>>> all.
>>> Lol. That actually sheds some light on your thought process:
>>> how do you suppose some property holds for all x, but not
>>> for every?
>> 
>> The set of all naturals is infinite but each and every natural is finite.
>
> Right. Well, just for fun... What about some strange shit like the infinite 
> ways to represent a natural?
>
> 1 = 4 - 3
> 1 = 2 + 1 - 2
> 1 = 2*4 - 7
> 1 = 4 - 2 - 1
> ...
>
> Forever...

Ah, number theory. You might enjoy this also:

https://en.wikipedia.org/wiki/Integer_partition