The technique was developed by G. Cantor to prove that the cardinality of the real numbers is greater than the cardinality of the integers. In this application the real numbers are enumerated in the form of a grid. A real number is then constructed, using the diagonal of the grid, that is not part of the original enumeration.
The technique was also used by J. Richard to generate a paradox about the namability of real numbers. This paradox (together with the “liar paradox” of antiquity) is reputed to have prompted K. Gödel to apply a similar technique of diagonalization in constructing a number-theory formula not provable in formal arithmetic. See Gödel's incompleteness theorems.
"diagonalization." A Dictionary of Computing. . Encyclopedia.com. (October 18, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/diagonalization
"diagonalization." A Dictionary of Computing. . Retrieved October 18, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/diagonalization
Encyclopedia.com 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, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com 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 Encyclopedia.com 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.