total order

English

Wikipedia

Noun

total order (plural total orders)

1. (set theory) A relation that is reflexive, antisymmetric, and transitive (i.e., that is a partial order), and having the property that for any two elements of its set, one is related to the other.

   If → is the material implication for a propositional logic $\mathcal{L}$, and $\mathcal{L}$ has logical equivalence ↔ (an equivalence relation), then → is a total order for the quotient $\mathcal{L} / \leftrightarrow$.

Synonyms

• total ordering relation (rare)

Hypernyms

• partial order
  • preorder

Hyponyms

• well-order

Related terms

• totally ordered set

Translations

relation

• Czech: lineární uspořádání (cs) n, úplné uspořádání (cs) n
• Esperanto: tuteca ordo (eo)

• Spanish: orden total (es) m