Talk:Countable set

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Countable vs counted

Some authors distinguish between a countable set and a counted set, a pair $(X,f)$ consisting of a set $X$ and a bijection between $X$ and (a subset of) the set $\mathbf{N}$ of natural numbers: the theorem that is mentioned then becomes that a counted union of counted sets is counted. Richard Pinch (talk) 20:44, 18 January 2018 (CET)

True; and the latter form of the theorem does not depend on the (countable) choice axiom, unlike the "usual" form. Boris Tsirelson (talk) 21:59, 18 January 2018 (CET)


  • T.E Forster, "Logic, Induction and Sets", Cambridge University Press (2003) ISBN 0-521-53361-9
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