Abstract
The equivalence relation of equipotence divides up any collection of sets into equivalence classes and the property that equipotent sets is called cardinal numbers. The cardinal numbers are a measure of the number of points in sets. Among the infinite sets, the denumerable numbers have the cardinal number. In set theory, an infinite set is a set that is not a finite set. The infinite sets can be countable or uncountable. A set that is equipotent to the set of natural numbers is called denumearble. A set that is either finite or denumerable is called countable. The set of all rational numbers is denumerable. The union of a denumerable number of denumerable sets is a denumerable set and every infinite set contains a denumerable subset. Therefore, every infinite set is equipotent to a proper subset of itself. The set of all real numbers is uncountable.
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