See asymptotic on Wiktionary
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Skof investigated an interesting asymptotic property of the additive functions (see Theorem 2.34). In fact, she proved that a function f : E₁ → E₂ is additive if and only if ‖f(x + y) − f(x) − f(y)‖ → 0 as ‖x‖ + ‖y‖ → ∞, where E₁ is a normed space and E₂ is a Banach space.", "type": "quote" }, { "ref": "2011, Vera Koponen, \"Some connections between finite, infinite model theory\", Finite and Algorithmic Model Theory, Cambridge University Press, →ISBN, page 110:", "text": "More recently, a direction of research initiated by Macpherson and Steinhorn [28] and continued by Elwes [13, 14] and Ryten studies classes of finite structures in which definable sets have a uniform asymptotic behaviour, as the cardinalities of the universes increase.", "type": "quote" } ], "glosses": [ "Pertaining to values or properties approached at infinity." ], "id": "en-asymptotic-en-adj-lXXxSPDR", "links": [ [ "mathematics", "mathematics" ], [ "value", "value" ], [ "properties", "property" ], [ "approach", "approach" ], [ "infinity", "infinity" ] ], "raw_glosses": [ "(mathematics) Pertaining to values or properties approached at infinity." ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ], "translations": [ { "_dis1": "88 12", "code": "ar", "lang": "Arabic", "roman": "muqārib", "sense": "pertaining to values or properties approached at infinity", "tags": [ "masculine" ], "word": "مُقَارِب" }, { "_dis1": "88 12", "code": "ca", "lang": "Catalan", "sense": "pertaining to values or properties approached at infinity", "word": "asimptòtic" }, { "_dis1": "88 12", "code": "cs", "lang": "Czech", "sense": "pertaining to values or properties approached at infinity", "word": "asymptotický" }, { "_dis1": "88 12", "code": "fi", "lang": "Finnish", "sense": "pertaining to values or properties approached at infinity", "word": "asymptoottinen" }, { "_dis1": "88 12", "code": "fr", "lang": "French", "sense": "pertaining to values or properties approached at infinity", "word": "asymptotique" }, { "_dis1": "88 12", "code": "de", "lang": "German", "sense": "pertaining to values or properties approached at infinity", "word": "asymptotisch" }, { "_dis1": "88 12", "code": "hu", "lang": "Hungarian", "sense": "pertaining to values or properties approached at infinity", "word": "aszimptotikus" }, { "_dis1": "88 12", "code": "it", "lang": "Italian", "sense": "pertaining to values or properties approached at infinity", "word": "asintotico" }, { "_dis1": "88 12", "alt": "ぜんきん", "code": "ja", "lang": "Japanese", "roman": "zenkin", "sense": "pertaining to values or properties approached at infinity", "word": "漸近" }, { "_dis1": "88 12", "code": "kk", "lang": "Kazakh", "roman": "asimptotikalyq", "sense": "pertaining to values or properties approached at infinity", "word": "асимптотикалық" }, { "_dis1": "88 12", "code": "pl", "lang": "Polish", "sense": "pertaining to values or properties approached at infinity", "word": "asymptotyczny" }, { "_dis1": "88 12", "code": "pt", "lang": "Portuguese", "sense": "pertaining to values or properties approached at infinity", "word": "assintótico" }, { "_dis1": "88 12", "code": "ro", "lang": "Romanian", "sense": "pertaining to values or properties approached at infinity", "tags": [ "masculine", "neuter" ], "word": "asimptotic" }, { "_dis1": "88 12", "code": "ru", "lang": "Russian", "roman": "asimptotíčeskij", "sense": "pertaining to values or properties approached at infinity", "word": "асимптоти́ческий" }, { "_dis1": "88 12", "code": "es", "lang": "Spanish", "sense": "pertaining to values or properties approached at infinity", "word": "asintótico" }, { "_dis1": "88 12", "code": "sv", "lang": "Swedish", "sense": "pertaining to values or properties approached at infinity", "word": "asymptotisk" }, { "_dis1": "88 12", "code": "cy", "lang": "Welsh", "sense": "pertaining to values or properties approached at infinity", "word": "asymptotig" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematical analysis", "orig": "en:Mathematical analysis", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "32 68", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "31 69", "kind": "other", "name": "English terms suffixed with -ic", "parents": [], "source": "w+disamb" }, { "_dis": "27 73", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "33 67", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "31 69", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "33 67", "kind": "other", "name": "Terms with Arabic translations", "parents": [], "source": "w+disamb" }, { "_dis": "32 68", "kind": "other", "name": "Terms with Catalan translations", "parents": [], "source": "w+disamb" }, { "_dis": "33 67", "kind": "other", "name": "Terms with Czech 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I Am In The Closet. I Am Not Coming Out.”, in Medium:", "text": "Because for some transwomen, femininity can feel asymptotic — the closer you get, the more you feel you can never make it.", "type": "quote" }, { "text": "The asymptotic behavior of a function" } ], "glosses": [ "Coming into consideration as a variable tends to a limit, usually infinity." ], "id": "en-asymptotic-en-adj-1KfIaamq", "links": [ [ "mathematical analysis", "mathematical analysis" ], [ "infinity", "infinity" ] ], "raw_glosses": [ "(mathematical analysis) Coming into consideration as a variable tends to a limit, usually infinity." ], "tags": [ "not-comparable" ], "topics": [ "mathematical-analysis", "mathematics", "sciences" ] } ], "sounds": [ { "ipa": "/ˌæsɪm(p)ˈtɒtɪk/", "tags": [ "UK" ] }, { "ipa": "/ˌæsəm(p)ˈtɑtɪk/", "tags": [ "US" ] }, { "ipa": "/ˌæsəm(p)ˈtɔtɪk/", "tags": [ "US" ] }, { "audio": "LL-Q1860 (eng)-Flame, not lame-asymptotic.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5c/LL-Q1860_%28eng%29-Flame%2C_not_lame-asymptotic.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-asymptotic.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5c/LL-Q1860_%28eng%29-Flame%2C_not_lame-asymptotic.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-asymptotic.wav.ogg" }, { "rhymes": "-ɒtɪk" } ], "synonyms": [ { "_dis1": "0 0", "word": "asymptotical" } ], "word": "asymptotic" }
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In fact, she proved that a function f : E₁ → E₂ is additive if and only if ‖f(x + y) − f(x) − f(y)‖ → 0 as ‖x‖ + ‖y‖ → ∞, where E₁ is a normed space and E₂ is a Banach space.", "type": "quote" }, { "ref": "2011, Vera Koponen, \"Some connections between finite, infinite model theory\", Finite and Algorithmic Model Theory, Cambridge University Press, →ISBN, page 110:", "text": "More recently, a direction of research initiated by Macpherson and Steinhorn [28] and continued by Elwes [13, 14] and Ryten studies classes of finite structures in which definable sets have a uniform asymptotic behaviour, as the cardinalities of the universes increase.", "type": "quote" } ], "glosses": [ "Pertaining to values or properties approached at infinity." ], "links": [ [ "mathematics", "mathematics" ], [ "value", "value" ], [ "properties", "property" ], [ "approach", "approach" ], [ "infinity", "infinity" ] ], "raw_glosses": [ "(mathematics) Pertaining to values or properties approached at infinity." ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ "English terms with quotations", "en:Mathematical analysis" ], "examples": [ { "ref": "2016 March 11, Jennifer Coates, “I Am A Transwoman. 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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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