On 6/21/2013 10:00 PM, Julio Di Egidio wrote: > "fom" <fomJUNK@nyms.net> wrote in message > news:X5CdnU5BCcfKQlnMnZ2dnUVZ_hadnZ2d@giganews.com...
> >> 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?