A set X is countable if there is a one-to-one correspondence between X and a subset of the set of natural numbers. Thus a countable set is either finite or denumerable. Some authors use ‘countable’ to solely mean denumerable.
Statistics
A set is countable if its members can be listed as a finite or infinite sequence, x1, x2,…. The rational numbers are countable, but the irrational numbers, even in a finite interval, are not.