FOM: Cantor's theorem of little interest in constructive math
Matthew Frank
mfrank at math.uchicago.edu
Tue Feb 13 15:38:51 EST 2001
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.
--Matt
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