See empty set in All languages combined, or Wiktionary
Download JSON data for empty set meaning in English (5.9kB)
{
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"kind": "topical",
"langcode": "en",
"name": "Set theory",
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"Fundamental"
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"examples": [
{
"ref": "1997, Reuben Hersh, What Is Mathematics, Really?, Oxford University Press, page 257",
"text": "Start with the empty set. We define it as “the set of all objects not equal to themselves,” since there are no such objects. All empty sets have the same members—no members at all! Therefore, as sets they're identical, by definition of identity of sets. In other words, there's only one empty set. This unique empty set is our building block. Next comes the set whose only member is—the empty set. This set is not empty.",
"type": "quotation"
},
{
"ref": "2004, Michael Potter, Set Theory and its Philosophy, Oxford University Press, page 58",
"text": "The existence of the empty set is entailed, in the presence of the axiom scheme of separation, by the existence of any set whatever.",
"type": "quotation"
},
{
"ref": "2007, A. K. Sharma, Measure Theory, Discovery Publishing House, page 1",
"text": "A topological space may be very sparsely endowed with open sets. As we know, some spaces have only two, the empty set and the full space.",
"type": "quotation"
},
{
"ref": "2008, Sam Gillespie, The Mathematics of Novelty: Badiou's Minimalist Metaphysics, re.press, page 57",
"text": "Their existence can be generated on the basis of the empty set, since one is simply the set of the empty set, two is simply that set plus the empty set and so forth.",
"type": "quotation"
}
],
"glosses": [
"The unique set that contains no elements, denoted ∅ or {}."
],
"id": "en-empty_set-en-noun-x4Mcq4hb",
"links": [
[
"set theory",
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[
"unique",
"unique"
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[
"element",
"element"
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[
"∅",
"∅#Translingual"
],
[
"{}",
"Unsupported titles/`lcub``rcub`#Translingual"
]
],
"raw_glosses": [
"(set theory) The unique set that contains no elements, denoted ∅ or {}."
],
"related": [
{
"word": "singleton set"
}
],
"synonyms": [
{
"sense": "set containing no elements",
"word": "null set"
}
],
"topics": [
"mathematics",
"sciences",
"set-theory"
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "kōngjí",
"sense": "unique set that contains no elements",
"word": "空集"
},
{
"code": "cs",
"lang": "Czech",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "prázdná množina"
},
{
"code": "da",
"lang": "Danish",
"sense": "unique set that contains no elements",
"word": "tomme mængde"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "unique set that contains no elements",
"word": "lege verzameling"
},
{
"code": "et",
"lang": "Estonian",
"sense": "unique set that contains no elements",
"word": "tühi hulk"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "unique set that contains no elements",
"word": "tyhjä joukko"
},
{
"code": "fr",
"lang": "French",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "ensemble vide"
},
{
"code": "gl",
"lang": "Galician",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "conxunto baleiro"
},
{
"code": "de",
"lang": "German",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "leere Menge"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "unique set that contains no elements",
"word": "üres halmaz"
},
{
"code": "it",
"lang": "Italian",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "insieme vuoto"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "kūshūgō",
"sense": "unique set that contains no elements",
"word": "空集合"
},
{
"code": "lv",
"lang": "Latvian",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "tukša kopa"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "prázno mnóžestvo",
"sense": "unique set that contains no elements",
"tags": [
"neuter"
],
"word": "пра́зно мно́жество"
},
{
"code": "pl",
"lang": "Polish",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "zbiór pusty"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "conjunto vazio"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "mulțime vidă"
},
{
"code": "ru",
"lang": "Russian",
"roman": "pustóje mnóžestvo",
"sense": "unique set that contains no elements",
"tags": [
"neuter"
],
"word": "пусто́е мно́жество"
},
{
"code": "es",
"lang": "Spanish",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "conjunto vacío"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "unique set that contains no elements",
"word": "tomma mängden"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "unique set that contains no elements",
"word": "walang-lamang tangkas"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "unique set that contains no elements",
"word": "tập hợp rỗng"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "unique set that contains no elements",
"word": "tập rỗng"
},
{
"code": "cy",
"lang": "Welsh",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "set wag"
}
],
"wikipedia": [
"empty set"
]
}
],
"word": "empty set"
}
{
"forms": [
{
"form": "empty sets",
"tags": [
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"head_templates": [
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"args": {},
"expansion": "empty set (plural empty sets)",
"name": "en-noun"
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{
"word": "singleton set"
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"English entries with incorrect language header",
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"examples": [
{
"ref": "1997, Reuben Hersh, What Is Mathematics, Really?, Oxford University Press, page 257",
"text": "Start with the empty set. We define it as “the set of all objects not equal to themselves,” since there are no such objects. All empty sets have the same members—no members at all! Therefore, as sets they're identical, by definition of identity of sets. In other words, there's only one empty set. This unique empty set is our building block. Next comes the set whose only member is—the empty set. This set is not empty.",
"type": "quotation"
},
{
"ref": "2004, Michael Potter, Set Theory and its Philosophy, Oxford University Press, page 58",
"text": "The existence of the empty set is entailed, in the presence of the axiom scheme of separation, by the existence of any set whatever.",
"type": "quotation"
},
{
"ref": "2007, A. K. Sharma, Measure Theory, Discovery Publishing House, page 1",
"text": "A topological space may be very sparsely endowed with open sets. As we know, some spaces have only two, the empty set and the full space.",
"type": "quotation"
},
{
"ref": "2008, Sam Gillespie, The Mathematics of Novelty: Badiou's Minimalist Metaphysics, re.press, page 57",
"text": "Their existence can be generated on the basis of the empty set, since one is simply the set of the empty set, two is simply that set plus the empty set and so forth.",
"type": "quotation"
}
],
"glosses": [
"The unique set that contains no elements, denoted ∅ or {}."
],
"links": [
[
"set theory",
"set theory"
],
[
"unique",
"unique"
],
[
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"element"
],
[
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"∅#Translingual"
],
[
"{}",
"Unsupported titles/`lcub``rcub`#Translingual"
]
],
"raw_glosses": [
"(set theory) The unique set that contains no elements, denoted ∅ or {}."
],
"topics": [
"mathematics",
"sciences",
"set-theory"
],
"wikipedia": [
"empty set"
]
}
],
"synonyms": [
{
"sense": "set containing no elements",
"word": "null set"
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "kōngjí",
"sense": "unique set that contains no elements",
"word": "空集"
},
{
"code": "cs",
"lang": "Czech",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "prázdná množina"
},
{
"code": "da",
"lang": "Danish",
"sense": "unique set that contains no elements",
"word": "tomme mængde"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "unique set that contains no elements",
"word": "lege verzameling"
},
{
"code": "et",
"lang": "Estonian",
"sense": "unique set that contains no elements",
"word": "tühi hulk"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "unique set that contains no elements",
"word": "tyhjä joukko"
},
{
"code": "fr",
"lang": "French",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "ensemble vide"
},
{
"code": "gl",
"lang": "Galician",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "conxunto baleiro"
},
{
"code": "de",
"lang": "German",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "leere Menge"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "unique set that contains no elements",
"word": "üres halmaz"
},
{
"code": "it",
"lang": "Italian",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "insieme vuoto"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "kūshūgō",
"sense": "unique set that contains no elements",
"word": "空集合"
},
{
"code": "lv",
"lang": "Latvian",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "tukša kopa"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "prázno mnóžestvo",
"sense": "unique set that contains no elements",
"tags": [
"neuter"
],
"word": "пра́зно мно́жество"
},
{
"code": "pl",
"lang": "Polish",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "zbiór pusty"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "conjunto vazio"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "mulțime vidă"
},
{
"code": "ru",
"lang": "Russian",
"roman": "pustóje mnóžestvo",
"sense": "unique set that contains no elements",
"tags": [
"neuter"
],
"word": "пусто́е мно́жество"
},
{
"code": "es",
"lang": "Spanish",
"sense": "unique set that contains no elements",
"tags": [
"masculine"
],
"word": "conjunto vacío"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "unique set that contains no elements",
"word": "tomma mängden"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "unique set that contains no elements",
"word": "walang-lamang tangkas"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "unique set that contains no elements",
"word": "tập hợp rỗng"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "unique set that contains no elements",
"word": "tập rỗng"
},
{
"code": "cy",
"lang": "Welsh",
"sense": "unique set that contains no elements",
"tags": [
"feminine"
],
"word": "set wag"
}
],
"word": "empty set"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.