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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? (infinitary)
Date: Sat, 19 Oct 2024 13:53:44 +0200
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On 19.10.2024 13:15, FromTheRafters wrote:
> WM was thinking very hard :
>> On 19.10.2024 12:56, Jim Burns wrote:

>>>> What is immediately before ω
>>> No number exists immediately before ω
>>
>> Immediately or not: The number before ω is finite.
> 
> No number is before omega,

In analysis we have to deal only with the infinitely small and the 
infinitely large as a limit-notion, as something becoming, emerging, 
produced, i.e., as we put it, with the potential infinite. [Hilbert].

All these becoming, emerging, produced numbers are numbers before ω. Are 
they produced from nothing or are they produced from hitherto dark 
numbers? If from nothing, then these numbers are the numbers before ω.

> omega is the naturally ordered set of natural 
> numbers.

That is another meaning of the word but not relevant, in particular not 
if there is no set of natural numbers because new numbers  can be 
produced and added.

>>> ω-1 can't be infinite and must be infinite.
>>
>> ω-1 is a natural number
> 
> No it is not.

ω-1 is a natural number if ℕ is a set, i.e., if no new numbers are 
produced from nothing.

Regards, WM