Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

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.