fom
Posts:
1,968
Registered:
12/4/12
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Re: Matheology § 288
Posted:
Jun 22, 2013 12:03 AM
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On 6/21/2013 10:00 PM, Julio Di Egidio wrote:
> "fom" <fomJUNK@nyms.net> wrote in message
> news:X5CdnU5BCcfKQlnMnZ2dnUVZ_hadnZ2d@giganews.com...
<snip>
>
>> I do not disagree that the naming of numbers
>> has a correspondence with the count of names.
>> But, because of Cantor's insights and investigations
>> of infinity, ordinality and cardinality are not
>> taken to be the same thing.
>
> I think that's beside the point. Anyway, those results do not
> (necessarily) hold in a non-standard setting.
>
Well, when Hilbert shifts from formal axiomatics
to finitistic proof theory, he begins with a
"strokes-as-numerals" intuition of natural number
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...
He then goes on to make the general argument for
cardinalities based upon the symmetric groups.
What non-standard setting conflates ordinality
and cardinality?
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