Working with the set of real numbers (was: Finding size of Variable)
Roy Smith
roy at panix.com
Wed Mar 5 05:25:37 CET 2014
In article <c39d5b44-6c7b-40d1-bbb5-791a36af6857 at googlegroups.com>,
Rustom Mody <rustompmody at gmail.com> wrote:
> I cannot find the exact quote so from memory Weyl says something to this
> effect:
>
> Cantor's diagonalization PROOF is not in question.
> Its CONCLUSION very much is.
> The classical/platonic mathematician (subject to wooly thinking) concludes
> that
> the real numbers are a superset of the integers
>
> The constructvist mathematician (who supposedly thinks clearly) only
> concludes
> the obvious, viz that real numbers cannot be enumerated
>
> To go from 'cannot be enumerated' to 'is a proper superset of' requires the
> assumption of 'completed infinities' and that is not math but theology
I stopped paying attention to mathematicians when they tried to convince
me that the sum of all natural numbers is -1/12. Sure, you can
manipulate the symbols in a way which is consistent with some set of
rules that we believe govern the legal manipulation of symbols, but it
just plain doesn't make sense.
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