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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 21:02:33 +0200
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On 19.10.2024 20:22, Alan Mackenzie wrote:
> WM <wolfgang.mueckenheim@tha.de> wrote:

> An infinite set is one which has a proper subset which can be
> put into 1-1 correspondence with the original set.  That is the
> definition.

According to Dedekind every set {1, 2, 3, ..., n} is in correspondence 
with the set {2, 4, 6, ..., 2n} which covers twice the interval, 
containing numbers not in the original set. This does not change when 
the whole set ℕ is multiplied by 2. The result covers twice the 
interval, containing numbers not in the original set ℕ.

Regards, WM