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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: Wed, 16 Oct 2024 17:26:26 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <e23a6c09c9ac9af53585ce969136a724c16e6a75@i2pn2.org>
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Am Wed, 16 Oct 2024 18:55:58 +0200 schrieb WM:
> On 16.10.2024 17:34, Jim Burns wrote:
>> On 10/16/2024 4:50 AM, WM wrote:
> 
>>>> There is a general rule not open to further discussion:
>>>> When doubling natural numbers we obtain natural numbers which have
>>>> not been doubled.
>>> CORRECTION:
>>> When doubling natural numbers we obtain even numbers which have not
>>> been doubled.
>> The set S of ordinals which are finite  and for which their double is
>> not finite is empty.
> Maybe. Then not all natural numbers have been doubled.
How do you mean?

>> When doubling natural numbers (finite ordinals)
>> we obtain natural numbers.
> Maybe.
Maybe?!

>> When doubling all natural numbers we obtain only natural numbers.
> That is impossible.
This is the same statement as above.

>>>> In potential infinity we obtain more even natural numbers than have
>>>> been doubled.
>>>> In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.
>> There is a general rule not open to further discussion:
>> The natural numbers ℕ equal the finite ordinals 𝕆ᶠⁱⁿ
> That is only possible in potential infinity. But there the result is
> worthless.
wtf "possible" "worthless" it is actually the case.

-- 
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.