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Re: Quetion about Cantor's Theorem
Posted:
May 9, 2011 2:50 PM
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Michael Stemper says...
>
>In article <iq3jjd0665@drn.newsguy.com>, stevendaryl3016@yahoo.com (Daryl
>McCullough) writes:
>>I think this might be a case of divergence between
>>intuitionistic logic and constructive logic.
>>Intuitionistic logic can (I think) prove that
>>every function from R to N must be constant.
>
>What? How about |ceil(x)| or floor(|y|) or
>f(x) = 17 if x<0 and 19 if x>0 or literally numberless other examples?
You can't prove that those define functions, intuitionistically.
For example, if you define a function f(x) = 17 if x < 0, and
f(x) = 19 if x >= 0, for you to be able to say that these two
clauses together define a function, you would need to be able
to prove:
forall reals x, x < 0 or x >= 0
which is not provable, intuitionistically.
--
Daryl McCullough
Ithaca, NY
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