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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?
Date: Sat, 21 Sep 2024 22:11:21 +0200
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On 21.09.2024 19:26, Jim Burns wrote:
> On 9/21/2024 9:47 AM, WM wrote:
>> On 20.09.2024 22:02, Jim Burns wrote:
>>> On 9/20/2024 2:27 PM, WM wrote:
> 
>>>> And there is no gap before ω.
>>>
>>> ω-1 requires impossibilities:
>>> a gap between ω and (hypothetical) ω-1
>>
>> No.
>> A gap is where something could be
>> but is not.
> 
> Gaps are where you locate your darkᵂᴹ numbers.

Yes.
> However,
> 'things always well.ordered' is
> what we mean by 'ordinals'.

That is a potentially infinite collection.
> There are no non.well.ordered WWMB ordinals.

That may be.
> 
> There is no finite WWMB ordinal α not.before
> the first transfinite ordinal, WWMB ω
> 
> There is no finite WWMB ordinal α without
> its WWMB successor α+1 before ω
> 
> There is no transfinite WWMB ordinal ξ before
> the first transfinite ordinal, WWMB ω

That may be. But then there is no complete set of natural numbers and no ω.

Regards, WM