Skip to main content


cardinality A measure of the size of a set. Two sets S and T have the same cardinality if there is a bijection from one to the other. S and T are said to be equipotent, often written as S ~ T. If the set S is finite, then the cardinality of S is the number of elements in the set. For an infinite set S, the idea of “number” of elements no longer suffices. An important fact, discovered by Cantor, is that not all infinite sets have the same cardinality. The two most important “grades” of infinite set can be illustrated as follows.

If S is equipotent to the set of natural numbers {1,2,3,…}

then S is said to have cardinality ℵ0 (a symbol called aleph null).

If S is equipotent to the set of real numbers then S is said to have cardinality C, or cardinality of the continuum. It can be shown that in some sense C = 2ℵ0

since the real numbers can be put in bijective correspondence with the set of all subsets of natural numbers.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"cardinality." A Dictionary of Computing. . 21 Mar. 2019 <>.

"cardinality." A Dictionary of Computing. . (March 21, 2019).

"cardinality." A Dictionary of Computing. . Retrieved March 21, 2019 from

Learn more about citation styles

Citation styles gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, cannot guarantee each citation it generates. Therefore, it’s best to use citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

The Chicago Manual of Style

American Psychological Association

  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.