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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Thu, 10 Oct 2024 19:54:32 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Thu, 10 Oct 2024 20:53:07 +0200 schrieb WM:
> On 10.10.2024 20:45, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
> 
>>> If all natnumbers are there and if 2n is greater than n, then the
>>> doubled numbers do not fit into ℕ.
>> For any finite n greater than zero, 2n is greater than n.  The same
>> does not hold for infinite n.
> There are no infinite n = natural numbers.
Exactly! There are furthermore no infinite doubles of naturals (2n).

>>>>> Numbers multiplied by 2 do not remain unchanged.
>>> Either doubling
>>> creates new natural numbers. Then not all have been doubled. Or all
>>> have been doubled, then some products fall outside of ℕ.
>> No.  Not even close.
> Deplorable. But note that all natural numbers are finite and follow this
> law: When doubled then 2n > n. If a set of natural numbers is doubled,
> then the results cover a larger set than before.
Additionally: if n is finite, so is 2n. It cannot go beyond w.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.