FOM: Cantor's theorem of little interest in constructive math
amah8857 at brain.math.fau.edu
Wed Feb 14 06:00:21 EST 2001
There can be one use of these cardinality theorem in mathematics, say, I
want to prove that two groups are non-isomorphic and
I settle the question as that the groups have different cardinality, I can
think of a proof like this but I don't know how important it is? Is it
possible to bypass the argument by showing a direct contradiction. Probably
it will be too case dependent to discuss generally.
But one place I know cardinality is definitely in use (correct me if I am
wrong) is that there are more Lebesgue measurable sets than Borel
measurable using the completeness of L-measure and the cantor set. Does
anybody know of any argument to bypass the obvious use of cardinality here.
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