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NNTP-Posting-Date: Tue, 27 Aug 2024 23:41:50 +0000
Subject: Re: Replacement of Cardinality (book-keeping sign)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Tue, 27 Aug 2024 16:41:55 -0700
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On 08/27/2024 04:06 PM, FromTheRafters wrote:
> WM wrote :
>> Le 25/08/2024 à 23:18, Jim Burns a écrit :
>>
>>> Therefore,
>>> there is no ω-1,
>>
>> If the set of ordinal numbers is complete, then ω-1 precedes ω - by
>> definition.
>
> What is the definition of subtraction here? Can you subtract past zero
> in the naturals?



You can build a little mound out past ten, say,
then relate that to zero in a sliding scale,
then if you find you can't remember how to roll the clock back,
you can count so many forward howsoever many were lost,
with a bit of book-keeping then it so results,
that the extra cost involved in counting over numbering,
lets you build the integers as deep as they are.