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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Simple enough for every reader?
Date: Tue, 24 Jun 2025 19:33:20 +0200
Organization: A noiseless patient Spider
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On 24.06.2025 11:15, Mikko wrote:
> On 2025-06-23 10:59:08 +0000, WM said:

>> The natural numbers are well-ordered, from the first to the last which 
>> is subtracted. Does this change if all can be subtracted?
> 
> There is no last natural number. Every subset of natural numbers
> has a first member (in the arithmetic order) but infinite subsets
> don't have a last one.

Then it is impossible to remove all of them in their order. But if it is 
possible to remove them completely, that cannot be done in their order. 
It can be done however in their order up to every definable number.
This shows the difference between definable and dark numbers.

Regards, WM