[{"word":"idempotent","phonetic":"/aɪ.dəmˈpoʊ.tənt/","phonetics":[{"text":"/aɪ.dəmˈpoʊ.tənt/","audio":""}],"meanings":[{"partOfSpeech":"noun","definitions":[{"definition":"An idempotent element.","synonyms":[],"antonyms":[]},{"definition":"An idempotent structure.","synonyms":[],"antonyms":[]}],"synonyms":[],"antonyms":[]},{"partOfSpeech":"adjective","definitions":[{"definition":"Said of a function: describing an action which, when performed multiple times on the same subject, has no further effect on its subject after the first time it is performed.","synonyms":[],"antonyms":[]},{"definition":"Said of an element of an algebraic structure with a binary operation (such as a group or semigroup): when the element operates on itself, the result is equal to itself.","synonyms":[],"antonyms":[],"example":"Every group has a unique idempotent element: namely, its identity element."},{"definition":"Said of a binary operation: that all of the distinct elements it can operate on are idempotent (in the sense given just above).","synonyms":[],"antonyms":[],"example":"Since the AND logical operator is commutative, associative, and idempotent, then it distributes with respect to itself."},{"definition":"Said of an algebraic structure: having an idempotent operation (in the sense above).","synonyms":[],"antonyms":[]}],"synonyms":[],"antonyms":[]}],"license":{"name":"CC BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"},"sourceUrls":["https://en.wiktionary.org/wiki/idempotent"]}]