"total order" meaning in English

See total order in All languages combined, or Wiktionary

Noun

Forms: total orders [plural]
Head templates: {{en-noun}} total order (plural total orders)
  1. (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). Wikipedia link: total order Categories (topical): Set theory Synonyms (partial order which applies an order to any two elements): linear order, linear ordering, total ordering, total ordering relation [rare] Hypernyms (partial order): preorder Hyponyms (partial order that applies an order to any two elements): well-order Related terms: totally ordered, totally ordered set, chain, connex property, connex relation, trichotomy Translations (partial order that applies an order to any two elements): lineární uspořádání [neuter] (Czech), úplné uspořádání [neuter] (Czech), tuteca ordo (Esperanto), täydellinen järjestys (Finnish), Totalordnung [feminine] (German), totale Ordnung [feminine] (German), orden total [masculine] (Spanish)

Inflected forms

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          "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.",
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          "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.",
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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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        "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)."
      ],
      "related": [
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          "word": "totally ordered"
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        {
          "word": "totally ordered set"
        },
        {
          "word": "chain"
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        {
          "word": "connex property"
        },
        {
          "word": "connex relation"
        },
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          "word": "trichotomy"
        }
      ],
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        {
          "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": [
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          "word": "total ordering relation"
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          "code": "cs",
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          "sense": "partial order that applies an order to any two elements",
          "tags": [
            "neuter"
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          "word": "lineární uspořádání"
        },
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          "code": "cs",
          "lang": "Czech",
          "sense": "partial order that applies an order to any two elements",
          "tags": [
            "neuter"
          ],
          "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"
        },
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          "lang": "Finnish",
          "sense": "partial order that applies an order to any two elements",
          "word": "täydellinen järjestys"
        },
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          "code": "de",
          "lang": "German",
          "sense": "partial order that applies an order to any two elements",
          "tags": [
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          ],
          "word": "Totalordnung"
        },
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          "code": "de",
          "lang": "German",
          "sense": "partial order that applies an order to any two elements",
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        },
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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": "total order"
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          "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.",
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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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    {
      "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": [
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      "word": "total ordering relation"
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    {
      "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"
      ],
      "word": "úplné uspořádání"
    },
    {
      "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"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "partial order that applies an order to any two elements",
      "tags": [
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      "word": "orden total"
    }
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  "word": "total order"
}

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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