Infinite sets
20-Dec-10
Within the logic of infinite sets, apparently larger infinite sets are actually the same size as seemingly smaller infinite sets. For example, the set of all natural numbers (1, 2, 3…) is the same size as the set of all even numbers (2, 4, 6…), though you might think it’d be twice the size, because the first natural number can be mapped onto the first even number, the second onto the second, and so on, to infinity, without any natural numbers left over.
via markvernon.com
I find this very hard to wrap my mind around, even though the logic seems sound.