FOM: Cantor's theorem of little interest in constructive math

Ayan amah8857 at
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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