# lexicographic order

## English[edit]

### Alternative forms[edit]

### Noun[edit]

**lexicographic order** (*plural* **lexicographic orders**)

- (mathematics) Formally, given two partially ordered sets A and B, the order ≤ on the Cartesian product A × B such that (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′).
- (mathematics) Given sets (A
_{1}, A_{2}, ..., A_{n}) and their total orderings (<_{1}, <_{2}, ..., <_{n}), the order <^{d}of A_{1}× A_{2}× ... × A_{n}such that (a_{1}, a_{2}, ..., a_{n}) <^{d}(b_{1},b_{2}, ..., b_{n}) iff (∃m > 0) (∀ i < m) (a_{i}= b_{i}) and (a_{m}<_{m}b_{m})

#### Usage notes[edit]

More generally, one can define the lexicographic order (a) on the Cartesian product of n ordered sets, (b) on the Cartesian product of a countably infinite family of ordered sets, and (c) on the union of such sets.