Re: does sqrt(2) exist in CM?
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Date: 02/06/05
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Date: 5 Feb 2005 18:43:58 -0800
Alan Smaill wrote:
> alex goldman <hello@spamm.er> writes:
>
> > Does Sqrt(2) exist in Constructive Mathematics? Proofs have to be
finite
> > AIUI, so unless we artificially augment the postulated objects,
irrational
> > numbers do not exist in CM.
>
> Yes, it is a constructive real number (AFAIK for all the various
> notions of constructive real).
>
> That means there is an algorithm that returns effectively
> converging rational approximations.
> The algorithm is a finite construct..
I agree that any computable real should be admissible in any
constructivist intepretation.
However, I think it's obvious that random reals are not. (Which is the
major source of headaches, those dirtly little numbers with necessarily
infinite representations)
Regards,
-- Eray Ozkural
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