A countable refers to something that can be counted or enumerated. In mathematics, a countable set is a set that has the same cardinality (size) as a subset of the natural numbers (positive integers). This means that the elements of a countable set can be put into a one-to-one correspondence with the natural numbers, allowing them to be counted in a systematic manner. Countable sets can be finite or infinite, but they must have a countable number of elements.