Finite sets are sets having a finite or countable number of elements. It is also known as countable sets as the elements present in them can be counted. Infinite sets in set theory are defined as sets that are not finite. The number of elements in an infinite set goes to infinity, that is, we cannot determine the exact number of elements. Infinite sets have ... either at the beginning or the ending of the list to indicate the set is uncountable and goes on forever.