See total order in All languages combined, or Wiktionary
Download JSON data for total order meaning in English (4.8kB)
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"ref": "2001, Vijay Kodiyalam, V. S. Sunder, Topological Quantum Field Theories from Subfactors, CRC Press (Chapman & Hall), page 2",
"text": "[…]we conclude §2.1 by showing how, given a triangulation #x5C;Delta (i.e., simplicial decomposition) of a closed oriented 3-manifilld M, and a total order '#x5C;le' on the set of vertices of #x5C;Delta, as well as a choice of a system #x5C;mathcal#x7B;B#x7D; of orthonormal bases for various Hilbert spaces that get specified in the process, we may obtain a complex number #x5C;langle(M,#x5C;Delta,#x5C;le,#x5C;mathcal#x7B;B#x7D;)#x5C;rangle.",
"type": "quotation"
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"ref": "2006, Daniel J. Velleman, How to Prove It: A Structured Approach, 2nd edition, Cambridge University Press, page 269",
"text": "Example 6.2.2. Suppose A is a finite set and R is a partial order on A. Prove that R can be extended to a total order on A. In other words, prove that there is a total order T on A such that R ⊆ T.",
"type": "quotation"
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{
"text": "2013, Nick Huggett, Tiziana Vistarini, Christian Wüthrich, 15: Time in Quantum Gravity, Adrian Bardon, Heather Dyke (editors), A Companion to the Philosophy of Time, Wiley, 2016, Paperback, page 245,\nA binary relation R defines a total order on a set X just in case for all x, y, z ∈ X, the following four conditions obtain: (1) Rxx (reflexivity), (2) Rxy & Ryz → Rxz (transitivity), (3) Rxy & Ryx → x = y (weak antisymmetry), and (4) Rxy ∨ Ryx (comparability). Bearing in mind that the relata of the total order are not events in ℰ, but entire equivalence classes ℰ/S of simultaneous events, it is straightforward to ask ≤ to be a total order of ℰ/S."
}
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"glosses": [
"A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x)."
],
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"sense": "partial order",
"word": "preorder"
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"sense": "partial order that applies an order to any two elements",
"word": "well-order"
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"(set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x)."
],
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"word": "totally ordered"
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"word": "totally ordered set"
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"word": "connex property"
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"word": "connex relation"
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"sense": "partial order which applies an order to any two elements",
"word": "linear order"
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"sense": "partial order which applies an order to any two elements",
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{
"sense": "partial order which applies an order to any two elements",
"word": "total ordering"
},
{
"sense": "partial order which applies an order to any two elements",
"tags": [
"rare"
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"word": "total ordering relation"
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"translations": [
{
"code": "cs",
"lang": "Czech",
"sense": "partial order that applies an order to any two elements",
"tags": [
"neuter"
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"word": "lineární uspořádání"
},
{
"code": "cs",
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"sense": "partial order that applies an order to any two elements",
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"word": "úplné uspořádání"
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{
"code": "eo",
"lang": "Esperanto",
"sense": "partial order that applies an order to any two elements",
"word": "tuteca ordo"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "partial order that applies an order to any two elements",
"word": "täydellinen järjestys"
},
{
"code": "de",
"lang": "German",
"sense": "partial order that applies an order to any two elements",
"tags": [
"feminine"
],
"word": "Totalordnung"
},
{
"code": "de",
"lang": "German",
"sense": "partial order that applies an order to any two elements",
"tags": [
"feminine"
],
"word": "totale Ordnung"
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{
"code": "es",
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"sense": "partial order that applies an order to any two elements",
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"word": "orden total"
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"word": "trichotomy"
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"ref": "2001, Vijay Kodiyalam, V. S. Sunder, Topological Quantum Field Theories from Subfactors, CRC Press (Chapman & Hall), page 2",
"text": "[…]we conclude §2.1 by showing how, given a triangulation #x5C;Delta (i.e., simplicial decomposition) of a closed oriented 3-manifilld M, and a total order '#x5C;le' on the set of vertices of #x5C;Delta, as well as a choice of a system #x5C;mathcal#x7B;B#x7D; of orthonormal bases for various Hilbert spaces that get specified in the process, we may obtain a complex number #x5C;langle(M,#x5C;Delta,#x5C;le,#x5C;mathcal#x7B;B#x7D;)#x5C;rangle.",
"type": "quotation"
},
{
"ref": "2006, Daniel J. Velleman, How to Prove It: A Structured Approach, 2nd edition, Cambridge University Press, page 269",
"text": "Example 6.2.2. Suppose A is a finite set and R is a partial order on A. Prove that R can be extended to a total order on A. In other words, prove that there is a total order T on A such that R ⊆ T.",
"type": "quotation"
},
{
"text": "2013, Nick Huggett, Tiziana Vistarini, Christian Wüthrich, 15: Time in Quantum Gravity, Adrian Bardon, Heather Dyke (editors), A Companion to the Philosophy of Time, Wiley, 2016, Paperback, page 245,\nA binary relation R defines a total order on a set X just in case for all x, y, z ∈ X, the following four conditions obtain: (1) Rxx (reflexivity), (2) Rxy & Ryz → Rxz (transitivity), (3) Rxy & Ryx → x = y (weak antisymmetry), and (4) Rxy ∨ Ryx (comparability). Bearing in mind that the relata of the total order are not events in ℰ, but entire equivalence classes ℰ/S of simultaneous events, it is straightforward to ask ≤ to be a total order of ℰ/S."
}
],
"glosses": [
"A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x)."
],
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"(set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x)."
],
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"synonyms": [
{
"sense": "partial order which applies an order to any two elements",
"word": "linear order"
},
{
"sense": "partial order which applies an order to any two elements",
"word": "linear ordering"
},
{
"sense": "partial order which applies an order to any two elements",
"word": "total ordering"
},
{
"sense": "partial order which applies an order to any two elements",
"tags": [
"rare"
],
"word": "total ordering relation"
}
],
"translations": [
{
"code": "cs",
"lang": "Czech",
"sense": "partial order that applies an order to any two elements",
"tags": [
"neuter"
],
"word": "lineární uspořádání"
},
{
"code": "cs",
"lang": "Czech",
"sense": "partial order that applies an order to any two elements",
"tags": [
"neuter"
],
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},
{
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"lang": "Esperanto",
"sense": "partial order that applies an order to any two elements",
"word": "tuteca ordo"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "partial order that applies an order to any two elements",
"word": "täydellinen järjestys"
},
{
"code": "de",
"lang": "German",
"sense": "partial order that applies an order to any two elements",
"tags": [
"feminine"
],
"word": "Totalordnung"
},
{
"code": "de",
"lang": "German",
"sense": "partial order that applies an order to any two elements",
"tags": [
"feminine"
],
"word": "totale Ordnung"
},
{
"code": "es",
"lang": "Spanish",
"sense": "partial order that applies an order to any two elements",
"tags": [
"masculine"
],
"word": "orden total"
}
],
"word": "total order"
}
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