for all x, y, and z in the domain of ◦. The law is known as the associative law. An expression involving several adjacent instances of an associative operation can be interpreted unambiguously; the order in which the operations are performed is irrelevant since the effects of different evaluations are identical, though the work involved may differ. Consequently parentheses are unnecessary, even in more complex expressions.
The arithmetic operations of addition and multiplication are associative, though subtraction is not. On a computer the associative law of addition of real numbers fails to hold because of the inherent inaccuracy in the way real numbers are usually represented (see floating-point notation), and the addition of integers fails to hold because of the possibility of overflow.
"associative operation." A Dictionary of Computing. . Encyclopedia.com. (October 22, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/associative-operation
"associative operation." A Dictionary of Computing. . Retrieved October 22, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/associative-operation
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.