total order

Noun

 * 1)  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).
 * 2) * 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 $$\mathcal{E}$$, but entire equivalence classes $$\mathcal{E}/S$$ of simultaneous events, it is straightforward to ask ≤ to be a total order of $$\mathcal{E}/S$$.
 * 1) * 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 $$\mathcal{E}$$, but entire equivalence classes $$\mathcal{E}/S$$ of simultaneous events, it is straightforward to ask ≤ to be a total order of $$\mathcal{E}/S$$.

Hypernyms

 * preorder
 * preorder
 * preorder

Translations

 * Czech: lineární uspořádání, úplné uspořádání
 * Esperanto: tuteca ordo
 * Finnish: täydellinen järjestys
 * German: Totalordnung, totale Ordnung
 * Spanish: orden total