English

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 , and has logical equivalence ↔ (an equivalence relation), then → is a total order for the quotient .

Synonyms

• linear order
• linear ordering
• total ordering
• total ordering relation (rare)

Hypernyms

• partial order
  • preorder

Hyponyms

• well-order

Related terms

• totally ordered set

Translations