# Talk:Countable set

From Encyclopedia of Mathematics

## 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)

#### References

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

**How to Cite This Entry:**

Countable set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Countable_set&oldid=42750