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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Contradiction of bijections as a measure for infinite sets
Date: Sun, 24 Mar 2024 17:10:34 -0400
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WM explained :
> Does ℕ = {1, 2, 3, ...} contain all natural numbers such that none can be 
> added?
>
> If so, then the bijection of ℕ with E = {2, 4, 6, ...} would prove that both 
> sets have the same number of elements.

Actually, same size set. "Number of elements" is better suited to 
finite sets.

> Then the completion of E resulting in 
> E = {1, 2, 3, 4, 5, 6, ...} would double the number of its elements.

That is not a completion of E. But still the same size set. By your 
sense of 'complete' the set of even numbers was already 'complete' 
because no more even numbers could be 'added'.

> Then there are more natural numbers than were originally in ℕ.

Nope.