# Countable Set

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An Countable Set is a set (with countable set members) that has a One-to-One Relation with the The N0 Natural Number Sequence.

## References

### 2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/countable_set Retrieved:2015-6-1.
• In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers. A countable set is either a finite set or a countably infinite set. Whether finite or infinite, the elements of a countable set can always be counted one at a time and, although the counting may never finish, every element of the set is associated with a natural number.

Some authors use countable set to mean infinitely countable alone.[1] To avoid this ambiguity, the term at most countable may be used when finite sets are included and countably infinite, enumerable, or denumerable[2] otherwise.

The term countable set was originated by Georg Cantor who contrasted sets which are countable with those which are uncountable (a.k.a. nonenumerable and nondenumerable[3]). Today, countable sets are researched by a branch of mathematics called discrete mathematics.

1. For an example of this usage see .
2. See .
3. See .