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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The
 non-existence of "dark numbers"]
Date: Sun, 13 Apr 2025 17:29:32 +0200
Organization: A noiseless patient Spider
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On 13.04.2025 14:00, FromTheRafters wrote:
> on 4/13/2025, WM supposed :

>> Bijections with ℕ are ordered by the well-ordered set ℕ.
> 
> The set N is not ordered, you want omega for the ordered set of naturals.

The well-ordered set ℕ is well ordered. Compare
§ 12.  Die wohlgeordneten Mengen ..... 312
§ 13.  Die Abschnitte wohlgeordneter Mengen .... 314
§ 14.  Die Ordnungszahlen wohlgeordneter Mengen ..  320
[Cantor, collected works]

Regards, WM