# total order

## EnglishEdit

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### NounEdit

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