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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 19:48:48 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Wed, 09 Oct 2024 18:47:39 +0200 schrieb WM:
> Am 09.10.2024 um 18:12 schrieb Alan Mackenzie:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
> 
>> You've misunderstood the nature of N.  The set is not {1, 2, 3, ...,
>> ω}, it is {1, 2, 3, ...}.
> I use ℕ U {ω} for clarity.
This makes it clear that w-1, w-2 and so on are not included.

>>> Should all places ω+2, ω+4, ω+6, ... remain empty?
>> It's not clear what you mean by this.  There are no such "places".
> According to Cantor they are there in actual infinity.
What are these "places"?

>>> Should the even numbers in spite of doubling remain below ω?
>> Yes, of course.
>>> Then they must occupy places not existing before.
>> No.  Remember the set is infinite, so you cannot use finite intuition
>> to reason about it.
> Numbers multiplied by 2 do not remain unchanged. That is not intuition
> but mathematics.
They do, however, remain natural.

-- 
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.