Size matters

Abstract
Does Cantorian set theory alter our intuitive conception of number? Yes. In particular, Cantorian set theory revises our intuitive conception of when two sets have the same size (cardinal number). Consider a variant of Galileo’s Paradox, which notes that the members of the set of natural numbers, N, can be put in one-to-one correspondence with the members of the set of even numbers, E.
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