See power set in All languages combined, or Wiktionary
{
"forms": [
{
"form": "power sets",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "power set (plural power sets)",
"name": "en-noun"
}
],
"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": "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 Czech translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Dutch 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 Hebrew translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Icelandic 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 Mandarin 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 Russian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Serbo-Croatian 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": "Set theory",
"orig": "en:Set theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"derived": [
{
"word": "hyper-power set"
}
],
"examples": [
{
"text": "The power set of #x5C;#x7B;1,2#x5C;#x7D; is #x5C;left#x5C;#x7B;#x5C;empty,#x5C;#x7B;1#x5C;#x7D;,#x5C;#x7B;2#x5C;#x7D;,#x5C;#x7B;1,2#x5C;#x7D;#x5C;right#x5C;#x7D;.",
"type": "example"
},
{
"ref": "2009, Arindama Singh, Elements of Computation Theory, Springer, page 16:",
"text": "Moreover, for notational convenience, we write the cardinality of a denumerable set as #x5C;aleph#x5F;0. Cardinality of the power set of a denumerable set is written as #x5C;aleph#x5F;1. We may thus extend this notation further by taking cardinality of the power set of the power set of a denumerable set as #x5C;aleph#x5F;2, etc. but we do not have the need for it right now.",
"type": "quote"
},
{
"ref": "2013, A. Carsetti, Epistemic Complexity and Knowledge Construction, Springer, page 94:",
"text": "Theorem 4.1. A complete Boolean algebra B has a set of (complete and atomic) ca-free generators iff B is isomorphic to the power set of a power set.",
"type": "quote"
},
{
"ref": "2015, Amir D. Aczel, Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers, Palgrave MacMillan, page 147:",
"text": "Exponentiation is essentially a move to the power set—the set of all subsets of a given set. This is one of the reasons why Bertrand Russell's paradox is indeed a paradox: We cannot find a universal set because no set can contain its own power set!",
"type": "quote"
}
],
"glosses": [
"The set whose elements comprise all the subsets of S (including the empty set and S itself)."
],
"id": "en-power_set-en-noun-18bB6ppp",
"links": [
[
"set theory",
"set theory"
],
[
"set",
"set"
],
[
"element",
"element"
],
[
"subset",
"subset"
],
[
"empty set",
"empty set"
]
],
"raw_glosses": [
"(set theory, of a set S) The set whose elements comprise all the subsets of S (including the empty set and S itself)."
],
"raw_tags": [
"of a set S"
],
"related": [
{
"word": "axiom of power set"
}
],
"synonyms": [
{
"tags": [
"attributive"
],
"word": "power-set"
},
{
"word": "powerset"
}
],
"topics": [
"mathematics",
"sciences",
"set-theory"
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "set of all subsets of a set",
"word": "冪集"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "mìjí",
"sense": "set of all subsets of a set",
"word": "幂集"
},
{
"code": "cs",
"lang": "Czech",
"sense": "set of all subsets of a set",
"tags": [
"feminine"
],
"word": "potenční množina"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "set of all subsets of a set",
"word": "machtenverzameling"
},
{
"code": "fr",
"lang": "French",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "ensemble des parties"
},
{
"code": "de",
"lang": "German",
"sense": "set of all subsets of a set",
"tags": [
"feminine"
],
"word": "Potenzmenge"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "k'vutzát khozká",
"sense": "set of all subsets of a set",
"tags": [
"feminine"
],
"word": "קבוצת חוזקה \\ קְבוּצַת חָזְקָה"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "set of all subsets of a set",
"word": "hatványhalmaz"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "set of all subsets of a set",
"tags": [
"neuter"
],
"word": "veldismengi"
},
{
"code": "it",
"lang": "Italian",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "insieme delle parti"
},
{
"code": "it",
"lang": "Italian",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "insieme potenza"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "bekishūgō",
"sense": "set of all subsets of a set",
"word": "冪集合"
},
{
"code": "pl",
"lang": "Polish",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "zbiór potęgowy"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "conjunto de partes"
},
{
"code": "ru",
"lang": "Russian",
"roman": "bulean",
"sense": "set of all subsets of a set",
"word": "булеан"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "partitivni skup"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "conjunto de partes"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "set of all subsets of a set",
"tags": [
"common-gender"
],
"word": "potensmängd"
}
],
"wikipedia": [
"Weierstrass p",
"power set"
]
}
],
"word": "power set"
}
{
"derived": [
{
"word": "hyper-power set"
}
],
"forms": [
{
"form": "power sets",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "power set (plural power sets)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "axiom of power set"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"English terms with usage examples",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with Czech translations",
"Terms with Dutch translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Hebrew translations",
"Terms with Hungarian translations",
"Terms with Icelandic translations",
"Terms with Italian translations",
"Terms with Japanese translations",
"Terms with Mandarin translations",
"Terms with Polish translations",
"Terms with Portuguese translations",
"Terms with Russian translations",
"Terms with Serbo-Croatian translations",
"Terms with Spanish translations",
"Terms with Swedish translations",
"en:Set theory"
],
"examples": [
{
"text": "The power set of #x5C;#x7B;1,2#x5C;#x7D; is #x5C;left#x5C;#x7B;#x5C;empty,#x5C;#x7B;1#x5C;#x7D;,#x5C;#x7B;2#x5C;#x7D;,#x5C;#x7B;1,2#x5C;#x7D;#x5C;right#x5C;#x7D;.",
"type": "example"
},
{
"ref": "2009, Arindama Singh, Elements of Computation Theory, Springer, page 16:",
"text": "Moreover, for notational convenience, we write the cardinality of a denumerable set as #x5C;aleph#x5F;0. Cardinality of the power set of a denumerable set is written as #x5C;aleph#x5F;1. We may thus extend this notation further by taking cardinality of the power set of the power set of a denumerable set as #x5C;aleph#x5F;2, etc. but we do not have the need for it right now.",
"type": "quote"
},
{
"ref": "2013, A. Carsetti, Epistemic Complexity and Knowledge Construction, Springer, page 94:",
"text": "Theorem 4.1. A complete Boolean algebra B has a set of (complete and atomic) ca-free generators iff B is isomorphic to the power set of a power set.",
"type": "quote"
},
{
"ref": "2015, Amir D. Aczel, Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers, Palgrave MacMillan, page 147:",
"text": "Exponentiation is essentially a move to the power set—the set of all subsets of a given set. This is one of the reasons why Bertrand Russell's paradox is indeed a paradox: We cannot find a universal set because no set can contain its own power set!",
"type": "quote"
}
],
"glosses": [
"The set whose elements comprise all the subsets of S (including the empty set and S itself)."
],
"links": [
[
"set theory",
"set theory"
],
[
"set",
"set"
],
[
"element",
"element"
],
[
"subset",
"subset"
],
[
"empty set",
"empty set"
]
],
"raw_glosses": [
"(set theory, of a set S) The set whose elements comprise all the subsets of S (including the empty set and S itself)."
],
"raw_tags": [
"of a set S"
],
"topics": [
"mathematics",
"sciences",
"set-theory"
],
"wikipedia": [
"Weierstrass p",
"power set"
]
}
],
"synonyms": [
{
"tags": [
"attributive"
],
"word": "power-set"
},
{
"word": "powerset"
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "set of all subsets of a set",
"word": "冪集"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "mìjí",
"sense": "set of all subsets of a set",
"word": "幂集"
},
{
"code": "cs",
"lang": "Czech",
"sense": "set of all subsets of a set",
"tags": [
"feminine"
],
"word": "potenční množina"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "set of all subsets of a set",
"word": "machtenverzameling"
},
{
"code": "fr",
"lang": "French",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "ensemble des parties"
},
{
"code": "de",
"lang": "German",
"sense": "set of all subsets of a set",
"tags": [
"feminine"
],
"word": "Potenzmenge"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "k'vutzát khozká",
"sense": "set of all subsets of a set",
"tags": [
"feminine"
],
"word": "קבוצת חוזקה \\ קְבוּצַת חָזְקָה"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "set of all subsets of a set",
"word": "hatványhalmaz"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "set of all subsets of a set",
"tags": [
"neuter"
],
"word": "veldismengi"
},
{
"code": "it",
"lang": "Italian",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "insieme delle parti"
},
{
"code": "it",
"lang": "Italian",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "insieme potenza"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "bekishūgō",
"sense": "set of all subsets of a set",
"word": "冪集合"
},
{
"code": "pl",
"lang": "Polish",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "zbiór potęgowy"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "conjunto de partes"
},
{
"code": "ru",
"lang": "Russian",
"roman": "bulean",
"sense": "set of all subsets of a set",
"word": "булеан"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "partitivni skup"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of all subsets of a set",
"tags": [
"masculine"
],
"word": "conjunto de partes"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "set of all subsets of a set",
"tags": [
"common-gender"
],
"word": "potensmängd"
}
],
"word": "power set"
}
Download raw JSONL data for power set meaning in English (5.3kB)
This page is a part of the kaikki.org machine-readable English 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.
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.