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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sun, 20 Oct 2024 10:31:52 -0400
Organization: Peripheral Visions
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WM formulated on Sunday :
> On 20.10.2024 14:20, Alan Mackenzie wrote:
>  > WM <wolfgang.mueckenheim@tha.de> wrote:
>
>  >> Say mapping or multiplying, it is a process. But that is not important.
>  >> Important is only that in the image there are numbers which have not
>  >> been mapped because 2n > n.
>  >
>  > That "because" attempts to connect two unrelated statements there are no
>  > "numbers which have not been mapped".  If you think there are, give an
>  > example.
>
> They can be proven by mathematics: Density reduced, fixed number, interval 
> enlarged.
>  >> If this is not accepted, then not all natural numbers of the image have
>  >> been in the original set.
>  >
>  > <Sigh>.  The sets are infinite.
>
> Infinite does not mean inaccessible to logic.

It also doesn't mean accessible to intuition. What you like to call 
logic, is merely your intuition which seems to be malfunctioning.