Difference between revisions of "Talk:Countable set"
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==Countable vs counted== | ==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. [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 20:44, 18 January 2018 (CET) | 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. [[User:Richard Pinch|Richard Pinch]] ([[User talk: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. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 21:59, 18 January 2018 (CET) | |
====References==== | ====References==== | ||
* T.E Forster, "Logic, Induction and Sets", Cambridge University Press (2003) ISBN 0-521-53361-9 | * T.E Forster, "Logic, Induction and Sets", Cambridge University Press (2003) ISBN 0-521-53361-9 | ||
Latest revision as of 20:59, 18 January 2018
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
Countable set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Countable_set&oldid=42750