See power set in All languages combined, or Wiktionary
Download JSON data for power set meaning in English (4.9kB)
{
"forms": [
{
"form": "power sets",
"tags": [
"plural"
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"args": {},
"expansion": "power set (plural power sets)",
"name": "en-noun"
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"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
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"source": "w"
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"kind": "topical",
"langcode": "en",
"name": "Set theory",
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],
"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": "quotation"
},
{
"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": "quotation"
},
{
"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": "quotation"
}
],
"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": [
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{
"args": {},
"expansion": "power set (plural power sets)",
"name": "en-noun"
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],
"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",
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"English terms with usage examples",
"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": "quotation"
},
{
"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": "quotation"
},
{
"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": "quotation"
}
],
"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"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 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.
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