# Countable set

## set with the same cardinality as some subset of the set of natural numbers / From Wikipedia, the free encyclopedia

In mathematics (particularly set theory), a **countable set** is a set whose elements can be counted. A set with one thing in it is countable, and so is a set with one hundred things in it. A set with all the natural numbers (counting numbers) in it is countable too. This is because even if it is infinite, someone who counts forever would not miss any of the numbers. The sets which has the same size as the natural numbers are therefore called countably infinite. The size of these sets are then written as $\aleph _{0}$(aleph-null)—the first of the aleph numbers.^{[1]} Sometimes when people say 'countable set' they mean countable and infinite.^{[2]} Georg Cantor coined the term.