FOM: Cantor's theorem
Stewart Shapiro
shapiro+ at osu.edu
Mon Feb 12 10:33:18 EST 2001
I have not yet followed the details of this most interesting thread
concerning Cantor's theorem. It might be noted that Bishop himself
mentions and proves Cantor's theorem in *Foundations of constructive
analysis*. As I recall, he gives the usual gloss on the theorem (that the
real numbers are not countable), and he gives a standard, diagonal
argument. To be sure, Bishop might have been mistaken about what is and
what is not constructively acceptable, but this citation is certainly
evidence that the proof is constructively kosher (assuming my memory is
correct--I have not had a chance to check this, and I wanted to get this
out before the thread goes cold. Sorry if someone already pointed this out).
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