total order

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Noun[edit]

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.

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