FOM: Re: Cantor's theorem of little interest in constructive math
alexzen at com2com.ru
Wed Feb 14 09:02:27 EST 2001
Without Cantor's theorem which is of little interest from your "norms for
constructive math" point of view, the notion itself of _uncountability_
makes no sense. As well as your "familiar, positive, typical example" as to
the proof of "the existence of a trascendental" according to that "the reals
are _uncountable_ and the algebraic reals are countable".
----- Original Message -----
From: Matthew Frank <mfrank at math.uchicago.edu>
To: <fom at math.psu.edu>
Sent: Tuesday, February 13, 2001 11:38 PM
Subject: FOM: Cantor's theorem of little interest in constructive math
> Cantor's theorem is of little interest in constructive math.
> At least, given my norms for constructive math, it ought to be of little
> interest. Set theory (as in the study of cardinals) and constructive math
> each have their own appeal, but I find the mixture unappealing.
> Here's a familiar, positive, typical example: Classically, one might
> prove the existence of a trascendental by noting that the reals are
> uncountable and the algebraic reals are countable. We don't use the
> cardinalities in a constructive proof because it is easy to construct a
> transcendental number directly.
More information about the FOM