>"If an infinite set can be put into one-to-one correspondence with the natural numbers (N) it is called a countable set. Otherwise it is uncountable."[1] This

>"If an infinite set can be put into one-to-one correspondence with the natural numbers (N) it is called a countable set. Otherwise it is uncountable."[1] This paradox hinges on the strange notion of cardinality of infinite sets. Specifically, the set of all even integers, the set of all odd integers, and the set of all integers(!) have the same cardinality, and therefore the same "size". --- [1]http://www.math.ups.edu/~bryans/Current/Journal_Spring_1999/mlaycock_300_s99.html http://www.math.ups.edu/~bryans/Current/Journal_Spring_1999/...