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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 09:59:07 +0200
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On 17.10.2024 21:39, FromTheRafters wrote:
> Anyway, the size of these infinite sets 
> are equal despite outpacing and asymtotic density considerations.

The even numbers and the natural numbers have the relative sizes

|{2, 4, 6, ..., 2n}|/|{1, 2, 3, 4, 5, 6, ..., 2n} = 1/2

for every n. Only real fools can believe that the relative size changes 
to 1 for all numbers |E|/|ℕ| = 1. Cantor knew this. Therefore 
cardinality is not true for the complete sets but only for potentially 
infinite initial segments.

Regards, WM