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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 10:16:21 +0200
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On 18.10.2024 00:34, Jim Burns wrote:
> On 10/17/2024 2:22 PM, WM wrote:

> A nonempty set without a first element
> is not a set of only finite ordinals.

The set of dark numbers contains only natural numbers.
What you call a "set of finite ordinals" is not a set but a potentially 
infinite collection.

Proof: If you double all your finite ordinals you obtain only finite 
ordinals again, although the covered interval is twice as large as the 
original interval covered by "all" your finite ordinals.

Regards, WM