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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: Sat, 19 Oct 2024 14:04:35 -0400
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WM has brought this to us :
> On 19.10.2024 16:24, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>
>>>> rather than the standard mathematical concept of a mapping from N -> N
>>>> where n is mapped to 2n.  In this standard notion, all numbers are
>>>> doubled, and we encounter no undoubled even natural numbers.
>> 
>>> Therefore the standard notion is wrong, if the natural numbers are a set.
>> 
>> You mean it's wrong because it doesn't gel with your intuition?
>
> No, it does not comply with mathematics. When multiplying all natural numbers 
> by 2, then the number of numbers remains the same but the density is reduced 
> and therefore the interval is doubled. 2 > n. Hence either natural numbers 
> are created which have not been multiplied, then ℕ is not a set, or other 
> numbers are created, then ℕ is a set.
>
>> If you think you can obtain an
>> "undoubled" number in that mapping, please feel free to give an example.
>
> I can prove it by 2n > n.
>
>> You can't, of course, you'll just say that all such are "dark numbers",
>
> Either dark numbers or natnumbers which have not been processed. There is no 
> other way because 2n > n.

Processed? Created? As I told you before, these are objects not 
projects.