Working with the set of real numbers (was: Finding size of Variable)

[Roy Smith]

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.