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Wiktionary英語版
出典：Wiktionary
total order
名詞
total order (複数形 total orders)
- (set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, かつ transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y または y ≤ x).
- 2001, Vijay Kodiyalam, V. S. Sunder, Topological Quantum Field Theories from Subfactors, CRC Press (Chapman & Hall), page 2,
- […] we conclude §2.1 by showing how, given a triangulation (i.e., simplicial decomposition) of a closed oriented 3-manifilld , and a total order '' on the set of vertices of , as well as a choice of a system of orthonormal bases for various Hilbert spaces that get specified in the process, we may obtain a complex number .
- 2006, Daniel J. Velleman, How to Prove It: A Structured Approach, Cambridge University Press, 2nd Edition, page 269,
- 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.
- 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,
- A 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 , but entire equivalence classes of simultaneous events, it is straightforward to ask ≤ to be a total order of .
- 2001, Vijay Kodiyalam, V. S. Sunder, Topological Quantum Field Theories from Subfactors, CRC Press (Chapman & Hall), page 2,
同意語
total-order
出典:『Wiktionary』 (2008/06/26 21:34 UTC 版)
ウィキペディア英語版
出典：Wikipedia
Total order
出典:『Wikipedia』 (2011/06/19 07:45 UTC 版)
英語による解説
ウィキペディア英語版からの引用
- 引用
In set theory, a total order, linear order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ≤) on some set X. The relation is transitive, antisymmetric, and total. A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain.
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Weblio英和・和英辞典に掲載されている「Wiktionary英語版」の記事は、Wiktionaryのtotal order (改訂履歴)、total-order (改訂履歴)の記事を複製、再配布したものにあたり、Creative Commons Attribution-ShareAlike (CC-BY-SA)もしくはGNU Free Documentation Licenseというライセンスの下で提供されています。
- Wikipedia
- Text is available under Creative Commons Attribution-ShareAlike (CC-BY-SA) and/or GNU Free Documentation License (GFDL).
Weblio英和・和英辞典に掲載されている「Wikipedia英語版」の記事は、WikipediaのTotal order (改訂履歴)の記事を複製、再配布したものにあたり、Creative Commons Attribution-ShareAlike (CC-BY-SA)もしくはGNU Free Documentation Licenseというライセンスの下で提供されています。
