See surjective on Wiktionary
{ "head_templates": [ { "args": { "1": "-" }, "expansion": "surjective (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 2 entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Catalan translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Danish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Dutch translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Irish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Japanese translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Mandarin translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Norwegian Bokmål translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Norwegian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Russian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "derived": [ { "word": "surjective function" }, { "word": "surjective map" } ], "examples": [ { "text": "1974, Thomas W. Hungerford, Algebra, Springer, page 5,\nA function f is surjective (or onto) provided f(A)=B; in other words,\nfor each b∈B,b=f(a) for some a∈A.\nA function f is said to be bijective (or a bijection or a one-to-one correspondence) if it is both injective and surjective." }, { "ref": "2010, Tullio Ceccherini-Silberstein, Michel Coornaert, Cellular Automata and Groups, Springer, page 133:", "text": "The Garden of Eden Theorem (Theorem 5.3.1) implies that every surjective cellular automaton with finite alphabet over an amenable group is necessarily pre-injective. In this section, we give an example of a surjective but not pre-injective cellular automaton with finite alphabet over the free group #x5C;textstyleF#x5F;2.", "type": "quote" }, { "ref": "2011, Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, 2nd edition, Springer, page 156:", "text": "This function is surjective and injective, and hence bijective.", "type": "quote" } ], "glosses": [ "Of, relating to, or being a surjection." ], "id": "en-surjective-en-adj-yWTu9TOS", "links": [ [ "mathematics", "mathematics" ], [ "surjection", "surjection" ] ], "raw_glosses": [ "(mathematics) Of, relating to, or being a surjection." ], "related": [ { "word": "surjection" }, { "word": "surjectivity" }, { "word": "bijective" }, { "word": "injective" } ], "synonyms": [ { "word": "onto" } ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "of, relating, or being a surjection", "word": "suprajectiu" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "mǎnshède", "sense": "of, relating, or being a surjection", "word": "满射的" }, { "code": "cs", "lang": "Czech", "sense": "of, relating, or being a surjection", "word": "surjektivní" }, { "code": "da", "lang": "Danish", "sense": "of, relating, or being a surjection", "word": "surjektiv" }, { "code": "nl", "lang": "Dutch", "sense": "of, relating, or being a surjection", "word": "surjectief" }, { "code": "fi", "lang": "Finnish", "sense": "of, relating, or being a surjection", "word": "surjektiivinen" }, { "code": "fr", "lang": "French", "sense": "of, relating, or being a surjection", "word": "surjectif" }, { "code": "de", "lang": "German", "sense": "of, relating, or being a surjection", "word": "surjektiv" }, { "code": "ga", "lang": "Irish", "sense": "of, relating, or being a surjection", "word": "barrtheilgeach" }, { "alt": "ぜんしゃの", "code": "ja", "lang": "Japanese", "roman": "zenshano", "sense": "of, relating, or being a surjection", "word": "全射の" }, { "code": "nb", "lang": "Norwegian Bokmål", "sense": "of, relating, or being a surjection", "word": "surjektiv" }, { "code": "no", "lang": "Norwegian Nynorsk", "sense": "of, relating, or being a surjection", "word": "surjektiv" }, { "code": "pl", "lang": "Polish", "sense": "of, relating, or being a surjection", "tags": [ "masculine" ], "word": "suriektywny" }, { "code": "pl", "lang": "Polish", "sense": "of, relating, or being a surjection", "tags": [ "feminine", "masculine", "neuter" ], "word": "na" }, { "code": "pt", "lang": "Portuguese", "sense": "of, relating, or being a surjection", "word": "sobrejetivo" }, { "code": "ro", "lang": "Romanian", "sense": "of, relating, or being a surjection", "word": "surjectiv" }, { "code": "ru", "lang": "Russian", "roman": "sjurʺjektivnyj", "sense": "of, relating, or being a surjection", "word": "сюръективный" }, { "code": "es", "lang": "Spanish", "sense": "of, relating, or being a surjection", "word": "sobreyectivo" }, { "code": "sv", "lang": "Swedish", "sense": "of, relating, or being a surjection", "word": "surjektiv" } ], "wikipedia": [ "surjective" ] } ], "sounds": [ { "ipa": "/səˈd͡ʒɛktɪv/", "tags": [ "Received-Pronunciation" ] }, { "ipa": "/sɚˈd͡ʒɛktɪv/", "tags": [ "General-American" ] }, { "rhymes": "-ɛktɪv" } ], "word": "surjective" } { "head_templates": [ { "args": { "1": "fr", "2": "adjective form" }, "expansion": "surjective", "name": "head" } ], "lang": "French", "lang_code": "fr", "pos": "adj", "senses": [ { "categories": [ { "kind": "other", "name": "French entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Pages with 2 entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" } ], "form_of": [ { "word": "surjectif" } ], "glosses": [ "feminine singular of surjectif" ], "id": "en-surjective-fr-adj-VJQ0wuCw", "links": [ [ "surjectif", "surjectif#French" ] ], "tags": [ "feminine", "form-of", "singular" ] } ], "sounds": [ { "ipa": "/syʁ.ʒɛk.tiv/" }, { "homophone": "surjectives" } ], "word": "surjective" }
{ "derived": [ { "word": "surjective function" }, { "word": "surjective map" } ], "head_templates": [ { "args": { "1": "-" }, "expansion": "surjective (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "related": [ { "word": "surjection" }, { "word": "surjectivity" }, { "word": "bijective" }, { "word": "injective" } ], "senses": [ { "categories": [ "English adjectives", "English entries with incorrect language header", "English lemmas", "English terms with quotations", "English uncomparable adjectives", "Entries with translation boxes", "Pages with 2 entries", "Pages with entries", "Rhymes:English/ɛktɪv", "Rhymes:English/ɛktɪv/3 syllables", "Terms with Catalan translations", "Terms with Czech translations", "Terms with Danish translations", "Terms with Dutch translations", "Terms with Finnish translations", "Terms with French translations", "Terms with German translations", "Terms with Irish translations", "Terms with Japanese translations", "Terms with Mandarin translations", "Terms with Norwegian Bokmål translations", "Terms with Norwegian translations", "Terms with Polish translations", "Terms with Portuguese translations", "Terms with Romanian translations", "Terms with Russian translations", "Terms with Spanish translations", "Terms with Swedish translations", "en:Mathematics" ], "examples": [ { "text": "1974, Thomas W. Hungerford, Algebra, Springer, page 5,\nA function f is surjective (or onto) provided f(A)=B; in other words,\nfor each b∈B,b=f(a) for some a∈A.\nA function f is said to be bijective (or a bijection or a one-to-one correspondence) if it is both injective and surjective." }, { "ref": "2010, Tullio Ceccherini-Silberstein, Michel Coornaert, Cellular Automata and Groups, Springer, page 133:", "text": "The Garden of Eden Theorem (Theorem 5.3.1) implies that every surjective cellular automaton with finite alphabet over an amenable group is necessarily pre-injective. In this section, we give an example of a surjective but not pre-injective cellular automaton with finite alphabet over the free group #x5C;textstyleF#x5F;2.", "type": "quote" }, { "ref": "2011, Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, 2nd edition, Springer, page 156:", "text": "This function is surjective and injective, and hence bijective.", "type": "quote" } ], "glosses": [ "Of, relating to, or being a surjection." ], "links": [ [ "mathematics", "mathematics" ], [ "surjection", "surjection" ] ], "raw_glosses": [ "(mathematics) Of, relating to, or being a surjection." ], "synonyms": [ { "word": "onto" } ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ], "wikipedia": [ "surjective" ] } ], "sounds": [ { "ipa": "/səˈd͡ʒɛktɪv/", "tags": [ "Received-Pronunciation" ] }, { "ipa": "/sɚˈd͡ʒɛktɪv/", "tags": [ "General-American" ] }, { "rhymes": "-ɛktɪv" } ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "of, relating, or being a surjection", "word": "suprajectiu" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "mǎnshède", "sense": "of, relating, or being a surjection", "word": "满射的" }, { "code": "cs", "lang": "Czech", "sense": "of, relating, or being a surjection", "word": "surjektivní" }, { "code": "da", "lang": "Danish", "sense": "of, relating, or being a surjection", "word": "surjektiv" }, { "code": "nl", "lang": "Dutch", "sense": "of, relating, or being a surjection", "word": "surjectief" }, { "code": "fi", "lang": "Finnish", "sense": "of, relating, or being a surjection", "word": "surjektiivinen" }, { "code": "fr", "lang": "French", "sense": "of, relating, or being a surjection", "word": "surjectif" }, { "code": "de", "lang": "German", "sense": "of, relating, or being a surjection", "word": "surjektiv" }, { "code": "ga", "lang": "Irish", "sense": "of, relating, or being a surjection", "word": "barrtheilgeach" }, { "alt": "ぜんしゃの", "code": "ja", "lang": "Japanese", "roman": "zenshano", "sense": "of, relating, or being a surjection", "word": "全射の" }, { "code": "nb", "lang": "Norwegian Bokmål", "sense": "of, relating, or being a surjection", "word": "surjektiv" }, { "code": "no", "lang": "Norwegian Nynorsk", "sense": "of, relating, or being a surjection", "word": "surjektiv" }, { "code": "pl", "lang": "Polish", "sense": "of, relating, or being a surjection", "tags": [ "masculine" ], "word": "suriektywny" }, { "code": "pl", "lang": "Polish", "sense": "of, relating, or being a surjection", "tags": [ "feminine", "masculine", "neuter" ], "word": "na" }, { "code": "pt", "lang": "Portuguese", "sense": "of, relating, or being a surjection", "word": "sobrejetivo" }, { "code": "ro", "lang": "Romanian", "sense": "of, relating, or being a surjection", "word": "surjectiv" }, { "code": "ru", "lang": "Russian", "roman": "sjurʺjektivnyj", "sense": "of, relating, or being a surjection", "word": "сюръективный" }, { "code": "es", "lang": "Spanish", "sense": "of, relating, or being a surjection", "word": "sobreyectivo" }, { "code": "sv", "lang": "Swedish", "sense": "of, relating, or being a surjection", "word": "surjektiv" } ], "word": "surjective" } { "head_templates": [ { "args": { "1": "fr", "2": "adjective form" }, "expansion": "surjective", "name": "head" } ], "lang": "French", "lang_code": "fr", "pos": "adj", "senses": [ { "categories": [ "French 3-syllable words", "French adjective forms", "French entries with incorrect language header", "French non-lemma forms", "French terms with IPA pronunciation", "French terms with homophones", "Pages with 2 entries", "Pages with entries" ], "form_of": [ { "word": "surjectif" } ], "glosses": [ "feminine singular of surjectif" ], "links": [ [ "surjectif", "surjectif#French" ] ], "tags": [ "feminine", "form-of", "singular" ] } ], "sounds": [ { "ipa": "/syʁ.ʒɛk.tiv/" }, { "homophone": "surjectives" } ], "word": "surjective" }
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