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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: Tue, 22 Oct 2024 18:12:44 +0200
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On 22.10.2024 18:03, Jim Burns wrote:
> On 10/22/2024 4:13 AM, WM wrote:

> ℕ is defined such that
> n ∈ ℕ  ⇔  ∃{0,1,...,n-1,n}

Most of all it is an invariable set with all its elements existing and 
subject to doubling.

> ∀n ∈ ℕ:  2×n ∈ ℕ

Not if all elements are existing before multiplication already.

Regards, WM