See tetration on Wiktionary
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The word was coined by the English mathematician Reuben Goodstein (1912–1985).", "forms": [ { "form": "tetrations", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "-", "2": "s" }, "expansion": "tetration (usually uncountable, plural tetrations)", "name": "en-noun" } ], "hyphenation": [ "tetr‧at‧ion" ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "English terms prefixed with tetra-", "parents": [], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Albanian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Bulgarian 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 Esperanto 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 Galician translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Hebrew translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Hungarian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Indonesian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Japanese translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Kazakh translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Korean translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Mandarin translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Marathi 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": "other", "name": "Terms with Turkish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Ukrainian translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Arithmetic", "orig": "en:Arithmetic", "parents": [ "Applied sciences", "Mathematics", "Sciences", "Formal sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Four", "orig": "en:Four", "parents": [ "Numbers", "All topics", "Terms by semantic function", "Fundamental" ], "source": "w" } ], "coordinate_terms": [ { "word": "addition" }, { "word": "exponentiation" }, { "word": "hexation" }, { "word": "multiplication" }, { "word": "pentation" }, { "word": "succession" }, { "word": "successor" }, { "alt": "augend", "english": "addend; total", "sense": "addition, summation", "word": "+ =" }, { "alt": "summand", "english": "sum", "sense": "addition, summation", "word": "+ +... =" }, { "english": "difference", "roman": "subtrahend", "sense": "subtraction", "word": "− =" }, { "english": "product", "roman": "multiplicand", "sense": "multiplication, factorization; multiplier", "word": "× =" }, { "english": "factor; factor; product", "sense": "multiplication, factorization; factor", "word": "× ×... =" }, { "roman": "quotient", "sense": "division; dividend", "word": "÷ =" }, { "alt": "quotient", "english": "with remaining", "sense": "numerator) / (denominator) = (quotient", "word": "Or sometimes" }, { "alt": "exponent", "english": "power", "sense": "exponentiation; base", "word": "=" }, { "roman": "radicand", "sense": "root extraction; degree", "tags": [ "root" ], "word": "√ =" }, { "alt": "antilogarithm", "english": "logarithm", "sense": "logarithmization", "word": "log(base) =" } ], "derived": [ { "word": "tetrational" } ], "examples": [ { "ref": "1982 May, Rudy Rucker, “All the Numbers”, in Infinity and the Mind: The Science and Philosophy of the Infinite, Boston, Mass.; Stuttgart, Baden-Württemberg: Birkhäuser, →ISBN, page 69:", "text": "You don't ordinarily hear much about tetration because it is so powerful an operation that tetrating even very small numbers with each other produces inordinately large numbers. A tetration is worked out below.\n⁴²#x3D;2#x7B;(2#x7B;(#x7B;2²#x7D;)#x7D;)#x7D;\n #x3D;2#x7B;(#x7B;2⁴#x7D;)#x7D;\n #x3D;2#x7B;16#x7D;\n #x3D;64,536", "type": "quote" }, { "ref": "1993, Alexander Humez, Nicholas Humez, Joseph Maguire, “One”, in Zero to Lazy Eight: The Romance of Numbers, New York, N.Y.: Touchstone, Simon & Schuster, →ISBN, page 39:", "text": "Repeated exponentiation—called tetration—is so rare that a shorthand for it is hardly worth the trouble, appealing only to research mathematicians. Most professional engineers and scientists never encounter tetration, and the shorthand for it is seldom taught anywhere but in mathematics departments. But it doesn't stop there, and for the almost-unheard-of \"multiple tetration\" there is yet a stronger cousin operation, waiting in the wings.", "type": "quote" }, { "ref": "2016, Erik Seligman, “Simple Surprises”, in Math Mutation Classics: Exploring Interesting, Fun and Weird Corners of Mathematics, New York, N.Y.: Apress, Springer Science+Business Media, →DOI, →ISBN, page 11:", "text": "Tetration is usually symbolized with a number drawn to the upper left of another number, as opposed to the upper right used for exponents. Let's look at an example: what is 2 tetrated to the 4th? We would draw this as a 2 with a little 4 to the upper left side: ⁴². This is equivalent to 2#x7B;2#x7B;2²", "type": "quote" } ], "glosses": [ "The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times." ], "id": "en-tetration-en-noun-52Mn3BgZ", "links": [ [ "arithmetic", "arithmetic" ], [ "arithmetic operator", "arithmetic operator" ], [ "consist", "consist" ], [ "repeated", "repeated#Adjective" ], [ "exponentiation", "exponentiation" ], [ "analogy", "analogy" ], [ "multiplication", "multiplication" ], [ "addition", "addition" ] ], "raw_glosses": [ "(arithmetic) The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times." ], "related": [ { "word": "tetrate" } ], "synonyms": [ { "word": "exponential map" }, { "word": "hyper4" }, { "word": "hyperpower" }, { "word": "power tower" }, { "word": "superexponentiation" } ], "tags": [ "uncountable", "usually" ], "topics": [ "arithmetic" ], "translations": [ { "code": "sq", "lang": "Albanian", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrimi" }, { "code": "bg", "lang": "Bulgarian", "roman": "tetracija", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "тетрация" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "超-4運算" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "chāo-4 yùnsuàn", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "超-4运算" }, { "code": "cs", "lang": "Czech", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrace" }, { "code": "da", "lang": "Danish", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetration" }, { "code": "nl", "lang": "Dutch", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetratie" }, { "code": "eo", "lang": "Esperanto", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "supereksponento" }, { "code": "fi", "lang": "Finnish", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetraatio" }, { "code": "fr", "lang": "French", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tétration" }, { "code": "gl", "lang": "Galician", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetración" }, { "code": "de", "lang": "German", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "Tetration" }, { "code": "de", "lang": "German", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "masculine" ], "word": "Potenzturm" }, { "code": "he", "lang": "Hebrew", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "טטרציה" }, { "code": "hu", "lang": "Hungarian", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetráció" }, { "code": "id", "lang": "Indonesian", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrasi" }, { "code": "it", "lang": "Italian", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetrazione" }, { "code": "ja", "lang": "Japanese", "roman": "tetorēshon", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "テトレーション" }, { "code": "kk", "lang": "Kazakh", "roman": "tetrasiä", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "тетрация" }, { "code": "kk", "lang": "Kazakh", "roman": "giperdäreje", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "гипердәреже" }, { "code": "ko", "lang": "Korean", "roman": "teteureisyeon", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "테트레이션" }, { "code": "mr", "lang": "Marathi", "roman": "ṭeṭreśan", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "टेट्रेशन" }, { "code": "pl", "lang": "Polish", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetracja" }, { "code": "pt", "lang": "Portuguese", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetração" }, { "code": "ro", "lang": "Romanian", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrația" }, { "code": "ru", "lang": "Russian", "roman": "tetrácija", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "тетра́ция" }, { "code": "es", "lang": "Spanish", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetración" }, { "code": "sv", "lang": "Swedish", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "common-gender" ], "word": "tetrering" }, { "code": "tr", "lang": "Turkish", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrasyon" }, { "code": "uk", "lang": "Ukrainian", "roman": "tetracija", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "тетрація" } ] } ], "sounds": [ { "ipa": "/tɛˈtɹeɪʃn̩/", "tags": [ "Received-Pronunciation" ] }, { "audio": "LL-Q1860 (eng)-Vealhurl-tetration.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/LL-Q1860_%28eng%29-Vealhurl-tetration.wav/LL-Q1860_%28eng%29-Vealhurl-tetration.wav.mp3", "ogg_url": 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The word was coined by the English mathematician Reuben Goodstein (1912–1985).", "forms": [ { "form": "tetrations", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "-", "2": "s" }, "expansion": "tetration (usually uncountable, plural tetrations)", "name": "en-noun" } ], "hyphenation": [ "tetr‧at‧ion" ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "tetrate" } ], "senses": [ { "categories": [ "English coinages", "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms coined by Reuben Goodstein", "English terms derived from the Proto-Indo-European word *kʷetwóres", "English terms prefixed with tetra-", "English terms with quotations", "English uncountable nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Requests for gender in Czech entries", "Requests for gender in Danish entries", "Requests for gender in Dutch entries", "Requests for gender in Hebrew entries", "Requests for gender in Romanian entries", "Requests for gender in Ukrainian entries", "Rhymes:English/eɪʃən", "Rhymes:English/eɪʃən/3 syllables", "Terms with Albanian translations", "Terms with Bulgarian translations", "Terms with Czech translations", "Terms with Danish translations", "Terms with Dutch translations", "Terms with Esperanto translations", "Terms with Finnish translations", "Terms with French translations", "Terms with Galician translations", "Terms with German translations", "Terms with Hebrew translations", "Terms with Hungarian translations", "Terms with Indonesian translations", "Terms with Italian translations", "Terms with Japanese translations", "Terms with Kazakh translations", "Terms with Korean translations", "Terms with Mandarin translations", "Terms with Marathi 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", "Terms with Turkish translations", "Terms with Ukrainian translations", "en:Arithmetic", "en:Four" ], "examples": [ { "ref": "1982 May, Rudy Rucker, “All the Numbers”, in Infinity and the Mind: The Science and Philosophy of the Infinite, Boston, Mass.; Stuttgart, Baden-Württemberg: Birkhäuser, →ISBN, page 69:", "text": "You don't ordinarily hear much about tetration because it is so powerful an operation that tetrating even very small numbers with each other produces inordinately large numbers. A tetration is worked out below.\n⁴²#x3D;2#x7B;(2#x7B;(#x7B;2²#x7D;)#x7D;)#x7D;\n #x3D;2#x7B;(#x7B;2⁴#x7D;)#x7D;\n #x3D;2#x7B;16#x7D;\n #x3D;64,536", "type": "quote" }, { "ref": "1993, Alexander Humez, Nicholas Humez, Joseph Maguire, “One”, in Zero to Lazy Eight: The Romance of Numbers, New York, N.Y.: Touchstone, Simon & Schuster, →ISBN, page 39:", "text": "Repeated exponentiation—called tetration—is so rare that a shorthand for it is hardly worth the trouble, appealing only to research mathematicians. Most professional engineers and scientists never encounter tetration, and the shorthand for it is seldom taught anywhere but in mathematics departments. But it doesn't stop there, and for the almost-unheard-of \"multiple tetration\" there is yet a stronger cousin operation, waiting in the wings.", "type": "quote" }, { "ref": "2016, Erik Seligman, “Simple Surprises”, in Math Mutation Classics: Exploring Interesting, Fun and Weird Corners of Mathematics, New York, N.Y.: Apress, Springer Science+Business Media, →DOI, →ISBN, page 11:", "text": "Tetration is usually symbolized with a number drawn to the upper left of another number, as opposed to the upper right used for exponents. Let's look at an example: what is 2 tetrated to the 4th? We would draw this as a 2 with a little 4 to the upper left side: ⁴². This is equivalent to 2#x7B;2#x7B;2²", "type": "quote" } ], "glosses": [ "The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times." ], "links": [ [ "arithmetic", "arithmetic" ], [ "arithmetic operator", "arithmetic operator" ], [ "consist", "consist" ], [ "repeated", "repeated#Adjective" ], [ "exponentiation", "exponentiation" ], [ "analogy", "analogy" ], [ "multiplication", "multiplication" ], [ "addition", "addition" ] ], "raw_glosses": [ "(arithmetic) The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times." ], "synonyms": [ { "word": "exponential map" }, { "word": "hyper4" }, { "word": "hyperpower" }, { "word": "power tower" }, { "word": "superexponentiation" } ], "tags": [ "uncountable", "usually" ], "topics": [ "arithmetic" ] } ], "sounds": [ { "ipa": "/tɛˈtɹeɪʃn̩/", "tags": [ "Received-Pronunciation" ] }, { "audio": "LL-Q1860 (eng)-Vealhurl-tetration.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/LL-Q1860_%28eng%29-Vealhurl-tetration.wav/LL-Q1860_%28eng%29-Vealhurl-tetration.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/LL-Q1860_%28eng%29-Vealhurl-tetration.wav/LL-Q1860_%28eng%29-Vealhurl-tetration.wav.ogg" }, { "ipa": "/tɛˈtɹeɪʃən/", "tags": [ "General-American" ] }, { "rhymes": "-eɪʃən" } ], "translations": [ { "code": "sq", "lang": "Albanian", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrimi" }, { "code": "bg", "lang": "Bulgarian", "roman": "tetracija", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "тетрация" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "超-4運算" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "chāo-4 yùnsuàn", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "超-4运算" }, { "code": "cs", "lang": "Czech", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrace" }, { "code": "da", "lang": "Danish", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetration" }, { "code": "nl", "lang": "Dutch", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetratie" }, { "code": "eo", "lang": "Esperanto", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "supereksponento" }, { "code": "fi", "lang": "Finnish", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetraatio" }, { "code": "fr", "lang": "French", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tétration" }, { "code": "gl", "lang": "Galician", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetración" }, { "code": "de", "lang": "German", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "Tetration" }, { "code": "de", "lang": "German", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "masculine" ], "word": "Potenzturm" }, { "code": "he", "lang": "Hebrew", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "טטרציה" }, { "code": "hu", "lang": "Hungarian", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetráció" }, { "code": "id", "lang": "Indonesian", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrasi" }, { "code": "it", "lang": "Italian", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetrazione" }, { "code": "ja", "lang": "Japanese", "roman": "tetorēshon", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "テトレーション" }, { "code": "kk", "lang": "Kazakh", "roman": "tetrasiä", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "тетрация" }, { "code": "kk", "lang": "Kazakh", "roman": "giperdäreje", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "гипердәреже" }, { "code": "ko", "lang": "Korean", "roman": "teteureisyeon", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "테트레이션" }, { "code": "mr", "lang": "Marathi", "roman": "ṭeṭreśan", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "टेट्रेशन" }, { "code": "pl", "lang": "Polish", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetracja" }, { "code": "pt", "lang": "Portuguese", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetração" }, { "code": "ro", "lang": "Romanian", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrația" }, { "code": "ru", "lang": "Russian", "roman": "tetrácija", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "тетра́ция" }, { "code": "es", "lang": "Spanish", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "feminine" ], "word": "tetración" }, { "code": "sv", "lang": "Swedish", "sense": "arithmetic operator consisting of repeated exponentiation", "tags": [ "common-gender" ], "word": "tetrering" }, { "code": "tr", "lang": "Turkish", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "tetrasyon" }, { "code": "uk", "lang": "Ukrainian", "roman": "tetracija", "sense": "arithmetic operator consisting of repeated exponentiation", "word": "тетрація" } ], "word": "tetration" }
Download raw JSONL data for tetration meaning in All languages combined (11.7kB)
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