cardinality of a countable union

Let $C$ be a countable collection of countable sets. Then $\cup C$ is countable.

Title cardinality of a countable union CardinalityOfACountableUnion 2013-03-22 11:59:59 2013-03-22 11:59:59 vampyr (22) vampyr (22) 5 vampyr (22) Theorem msc 03E10 A_nAreCountableSoIsA_1XXA_nIfA_1