See supremum in All languages combined, or Wiktionary
Download JSON data for supremum meaning in English (5.7kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "la",
"3": "supremum"
},
"expansion": "Latin supremum",
"name": "bor"
}
],
"etymology_text": "Borrowed from Latin supremum.",
"forms": [
{
"form": "supremums",
"tags": [
"plural"
]
},
{
"form": "suprema",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "s",
"2": "suprema"
},
"expansion": "supremum (plural supremums or suprema)",
"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": "English entries with topic categories using raw markup",
"parents": [
"Entries with topic categories using raw markup",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Japanese terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Set theory",
"orig": "en:Set theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"coordinate_terms": [
{
"word": "infimum"
}
],
"derived": [
{
"word": "essential supremum"
}
],
"examples": [
{
"ref": "2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd edition, Springer, page 8",
"text": "A sublattice of a lattice is a subset that is closed under pairwise infima and suprema.",
"type": "quotation"
},
{
"ref": "2010, James S. Howland, Basic Real Analysis, Jones & Bartlett Publishers, page 9",
"text": "The best way to describe the supremum of S is to say that it wants to be the greatest element of S. In fact, if S has a greatest element, then that element is the supremum.",
"type": "quotation"
},
{
"ref": "2011, Andreas Löhne, Vector Optimization with Infimum and Supremum, Springer, page vii",
"text": "The key to an approach to vector optimization based on infimum and supremum is to consider set-based objective functions and to extend the partial ordering of the original objective space to a suitable subspace of the power set. In this new space the infimum and supremum exist under the usual assumptions.",
"type": "quotation"
}
],
"glosses": [
"(real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y."
],
"id": "en-supremum-en-noun-vjQnmN-1",
"links": [
[
"Wikipedia",
"Wikipedia"
],
[
"supremum",
"w:supremum"
],
[
"set theory",
"set theory"
],
[
"subset",
"subset"
],
[
"real number",
"real number"
],
[
"partially ordered set",
"partially ordered set"
],
[
"partial order",
"partial order"
],
[
"least",
"least"
]
],
"raw_glosses": [
"(set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y."
],
"related": [
{
"word": "maximum"
}
],
"synonyms": [
{
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "least upper bound"
},
{
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "LUB"
},
{
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "sup"
}
],
"topics": [
"mathematics",
"sciences",
"set-theory"
],
"translations": [
{
"code": "cs",
"lang": "Czech",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"neuter"
],
"word": "supremum"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "pienin yläraja"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "supremum"
},
{
"code": "fr",
"lang": "French",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "supremum"
},
{
"code": "de",
"lang": "German",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"neuter"
],
"word": "Supremum"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "סופרמום"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "חסם עליון"
},
{
"alt": "じょうげん",
"code": "ja",
"lang": "Japanese",
"roman": "jōgen",
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "上限"
},
{
"code": "pl",
"lang": "Polish",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"neuter"
],
"word": "supremum"
},
{
"code": "pl",
"lang": "Polish",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "kres górny"
},
{
"code": "es",
"lang": "Spanish",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "supremo"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "supremum"
}
]
}
],
"word": "supremum"
}
{
"coordinate_terms": [
{
"word": "infimum"
}
],
"derived": [
{
"word": "essential supremum"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "la",
"3": "supremum"
},
"expansion": "Latin supremum",
"name": "bor"
}
],
"etymology_text": "Borrowed from Latin supremum.",
"forms": [
{
"form": "supremums",
"tags": [
"plural"
]
},
{
"form": "suprema",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "s",
"2": "suprema"
},
"expansion": "supremum (plural supremums or suprema)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "maximum"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with topic categories using raw markup",
"English lemmas",
"English nouns",
"English nouns with irregular plurals",
"English terms borrowed from Latin",
"English terms derived from Latin",
"English terms with quotations",
"Japanese terms with redundant script codes",
"en:Algebra",
"en:Mathematical analysis",
"en:Set theory"
],
"examples": [
{
"ref": "2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd edition, Springer, page 8",
"text": "A sublattice of a lattice is a subset that is closed under pairwise infima and suprema.",
"type": "quotation"
},
{
"ref": "2010, James S. Howland, Basic Real Analysis, Jones & Bartlett Publishers, page 9",
"text": "The best way to describe the supremum of S is to say that it wants to be the greatest element of S. In fact, if S has a greatest element, then that element is the supremum.",
"type": "quotation"
},
{
"ref": "2011, Andreas Löhne, Vector Optimization with Infimum and Supremum, Springer, page vii",
"text": "The key to an approach to vector optimization based on infimum and supremum is to consider set-based objective functions and to extend the partial ordering of the original objective space to a suitable subspace of the power set. In this new space the infimum and supremum exist under the usual assumptions.",
"type": "quotation"
}
],
"glosses": [
"(real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y."
],
"links": [
[
"Wikipedia",
"Wikipedia"
],
[
"supremum",
"w:supremum"
],
[
"set theory",
"set theory"
],
[
"subset",
"subset"
],
[
"real number",
"real number"
],
[
"partially ordered set",
"partially ordered set"
],
[
"partial order",
"partial order"
],
[
"least",
"least"
]
],
"raw_glosses": [
"(set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y."
],
"topics": [
"mathematics",
"sciences",
"set-theory"
]
}
],
"synonyms": [
{
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "least upper bound"
},
{
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "LUB"
},
{
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "sup"
}
],
"translations": [
{
"code": "cs",
"lang": "Czech",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"neuter"
],
"word": "supremum"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "pienin yläraja"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "supremum"
},
{
"code": "fr",
"lang": "French",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "supremum"
},
{
"code": "de",
"lang": "German",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"neuter"
],
"word": "Supremum"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "סופרמום"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "חסם עליון"
},
{
"alt": "じょうげん",
"code": "ja",
"lang": "Japanese",
"roman": "jōgen",
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "上限"
},
{
"code": "pl",
"lang": "Polish",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"neuter"
],
"word": "supremum"
},
{
"code": "pl",
"lang": "Polish",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "kres górny"
},
{
"code": "es",
"lang": "Spanish",
"sense": "element of a set greater than or equal to all members of a given subset",
"tags": [
"masculine"
],
"word": "supremo"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "element of a set greater than or equal to all members of a given subset",
"word": "supremum"
}
],
"word": "supremum"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-18 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). 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.