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Cardinal and Ordinal Numbers

1964; Elsevier BV; Linguagem: Inglês

10.1016/b978-1-4832-0012-5.50007-1

William J. Pervin,

Logic, Reasoning, and Knowledge

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.