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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 2 Nov 2024 16:34:29 -0400
Organization: i2pn2 (i2pn.org)
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On 11/2/24 1:42 PM, WM wrote:
> 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.
> 
> Regards, WM
> 

But if it applies to ALL, it must apply to ANY, so a property of ANY 
must apply to each on of the ALL.

So, for ALL the Natural Numbers, there can't be a highest, because for 
ANY Natural Number there is a following one, and if there was a Highest, 
it would have a property that NONE of the Natural Numbers have (not 
having a successor) so it couldn't have been a Natural Number.