See triangle inequality on Wiktionary
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"(mathematical analysis) The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors." ], "topics": [ "mathematical-analysis", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematical analysis", "orig": "en:Mathematical analysis", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "22 49 29", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "25 51 25", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "23 51 26", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "17 58 25", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" 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"other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" }, { "_dis": "23 55 22", "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w+disamb" }, { "_dis": "20 59 21", "kind": "other", "name": "Terms with Russian translations", "parents": [], "source": "w+disamb" }, { "_dis": "17 64 18", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" }, { "_dis": "23 54 23", "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w+disamb" } ], "examples": [ { "text": "d(x,z)≤d(x,y)+d(y,z)" } ], "glosses": [ "The inequality that states that the distance between two points is less than or equal to the sum of the distances between the first two points and some third point." ], "head_nr": 2, "id": "en-triangle_inequality-en-name-OSf3x2Tz", "links": [ [ "mathematical analysis", "mathematical analysis" ], [ "inequality", "inequality" ], [ "distance", "distance" ], [ "point", "point" ] ], "raw_glosses": [ "(mathematical analysis) The inequality that states that the distance between two points is less than or equal to the sum of the distances between the first two points and some third point." ], "topics": [ "mathematical-analysis", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematical analysis", "orig": "en:Mathematical analysis", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Either of the above two inequalities, considered as one of the axioms which a function must satisfy to be a norm or metric respectively." ], "head_nr": 2, "id": "en-triangle_inequality-en-name-zfCx4Ont", "links": [ [ "mathematical analysis", "mathematical analysis" ], [ "abstraction", "abstraction" ], [ "axiom", "axiom" ], [ "norm", "norm" ], [ "metric", "metric" ] ], "qualifier": "by abstraction", "raw_glosses": [ "(mathematical analysis, by abstraction) Either of the above two inequalities, considered as one of the axioms which a function must satisfy to be a norm or metric respectively." ], "topics": [ "mathematical-analysis", "mathematics", "sciences" ] } ], "translations": [ { "_dis1": "44 44 11", "code": "zh", "lang": "Chinese", "roman": "sānjiǎo bùděngshì", "sense": "the triangle inequality", "word": "三角不等式" }, { "_dis1": "44 44 11", "code": "fi", "lang": "Finnish", "sense": "the triangle inequality", "word": "kolmioepäyhtälö" }, { "_dis1": "44 44 11", "code": "fr", "lang": "French", "sense": "the triangle inequality", "tags": [ "feminine" ], "word": "inégalité triangulaire" }, { "_dis1": "44 44 11", "code": "de", "lang": "German", "sense": "the triangle inequality", "tags": [ "feminine" ], "word": "Dreiecksungleichung" }, { "_dis1": "44 44 11", "code": "he", "lang": "Hebrew", "sense": "the triangle inequality", "word": "אי שוויון המשולש" }, { "_dis1": "44 44 11", "code": "it", "lang": "Italian", "sense": "the triangle inequality", "tags": [ "feminine" ], "word": "disuguaglianza triangolare" }, { "_dis1": "44 44 11", "alt": "さんかくふとうしき", "code": "ja", "lang": "Japanese", "roman": "sankaku futōshiki", "sense": "the triangle inequality", "word": "三角不等式" }, { "_dis1": "44 44 11", "code": "pl", "lang": "Polish", "sense": "the triangle inequality", "tags": [ "feminine" ], "word": "nierówność trójkąta" }, { "_dis1": "44 44 11", "code": "pt", "lang": "Portuguese", "sense": "the triangle inequality", "tags": [ "feminine" ], "word": "desigualdade triangular" }, { "_dis1": "44 44 11", "code": "ro", "lang": "Romanian", "note": "def. form", "sense": "the triangle inequality", "tags": [ "feminine" ], "word": "inegalitatea triunghiului" }, { "_dis1": "44 44 11", "code": "ru", "lang": "Russian", "roman": "nerávenstvo treugólʹnika", "sense": "the triangle inequality", "tags": [ "neuter" ], "word": "нера́венство треуго́льника" }, { "_dis1": "44 44 11", "code": "es", "lang": "Spanish", "sense": "the triangle inequality", "tags": [ "feminine" ], "word": "desigualdad del triángulo" }, { "_dis1": "44 44 11", "code": "sv", "lang": "Swedish", "sense": "the triangle inequality", "tags": [ "common-gender" ], "word": "triangelolikhet" } ], "wikipedia": [ "triangle inequality" ], "word": "triangle inequality" }
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