See extensionality in All languages combined, or Wiktionary
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{ "etymology_templates": [ { "args": { "1": "en", "2": "extensional", "3": "ity" }, "expansion": "extensional + -ity", "name": "suffix" } ], "etymology_text": "extensional + -ity", "forms": [ { "form": "extensionalities", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "-", "2": "+" }, "expansion": "extensionality (usually uncountable, plural extensionalities)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "_dis1": "0 0 0", "word": "extensionalism" } ], "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Philosophy", "orig": "en:Philosophy", "parents": [ "All topics", "Fundamental" ], "source": "w" }, { "_dis": "33 29 38", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "34 30 36", "kind": "other", "name": "English terms suffixed with -ity", "parents": [], "source": "w+disamb" } ], "glosses": [ "The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties." ], "id": "en-extensionality-en-noun-8~k4qq7Q", "links": [ [ "philosophy", "philosophy" ] ], "raw_glosses": [ "(philosophy) The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties." ], "tags": [ "uncountable", "usually" ], "topics": [ "human-sciences", "philosophy", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Functional analysis", "orig": "en:Functional analysis", "parents": [ "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "33 29 38", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "34 30 36", "kind": "other", "name": "English terms suffixed with -ity", "parents": [], "source": "w+disamb" } ], "glosses": [ "The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same." ], "id": "en-extensionality-en-noun-B4U4UR9Z", "links": [ [ "mathematics", "mathematics" ], [ "functional analysis", "functional analysis" ], [ "function", "function" ], [ "domain", "domain" ] ], "qualifier": "functional analysis", "raw_glosses": [ "(mathematics, functional analysis) The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same." ], "tags": [ "uncountable", "usually" ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Set theory", "orig": "en:Set theory", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "33 29 38", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "34 30 36", "kind": "other", "name": "English terms suffixed with -ity", "parents": [], "source": "w+disamb" } ], "glosses": [ "The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements." ], "id": "en-extensionality-en-noun-mpA2Tzn7", "links": [ [ "mathematics", "mathematics" ], [ "set theory", "set theory" ], [ "axiom of extensionality", "axiom of extensionality" ] ], "raw_glosses": [ "(mathematics, set theory) The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements." ], "tags": [ "uncountable", "usually" ], "topics": [ "mathematics", "sciences", "set-theory" ] } ], "translations": [ { "_dis1": "37 32 31", "code": "pl", "lang": "Polish", "sense": "the principle of distinguishing only by externally observable properties", "word": "ekstensjonalność" } ], "word": "extensionality" }
{ "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms suffixed with -ity", "English uncountable nouns" ], "etymology_templates": [ { "args": { "1": "en", "2": "extensional", "3": "ity" }, "expansion": "extensional + -ity", "name": "suffix" } ], "etymology_text": "extensional + -ity", "forms": [ { "form": "extensionalities", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "-", "2": "+" }, "expansion": "extensionality (usually uncountable, plural extensionalities)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "extensionalism" } ], "senses": [ { "categories": [ "en:Philosophy" ], "glosses": [ "The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties." ], "links": [ [ "philosophy", "philosophy" ] ], "raw_glosses": [ "(philosophy) The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties." ], "tags": [ "uncountable", "usually" ], "topics": [ "human-sciences", "philosophy", "sciences" ] }, { "categories": [ "en:Functional analysis", "en:Mathematics" ], "glosses": [ "The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same." ], "links": [ [ "mathematics", "mathematics" ], [ "functional analysis", "functional analysis" ], [ "function", "function" ], [ "domain", "domain" ] ], "qualifier": "functional analysis", "raw_glosses": [ "(mathematics, functional analysis) The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same." ], "tags": [ "uncountable", "usually" ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ "en:Mathematics", "en:Set theory" ], "glosses": [ "The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements." ], "links": [ [ "mathematics", "mathematics" ], [ "set theory", "set theory" ], [ "axiom of extensionality", "axiom of extensionality" ] ], "raw_glosses": [ "(mathematics, set theory) The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements." ], "tags": [ "uncountable", "usually" ], "topics": [ "mathematics", "sciences", "set-theory" ] } ], "translations": [ { "code": "pl", "lang": "Polish", "sense": "the principle of distinguishing only by externally observable properties", "word": "ekstensjonalność" } ], "word": "extensionality" }
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