# Category:Lexicographic Order

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This category contains results about Lexicographic Order.

Definitions specific to this category can be found in Definitions/Lexicographic Order.

Let $\struct {S_1, \preceq_1}$ and $\struct {S_2, \preceq_2}$ be ordered sets.

The **lexicographic order on $S_1 \times S_2$** is the relation $\preccurlyeq$ defined on $S_1 \times S_2$ as:

- $\tuple {x_1, x_2} \preccurlyeq \tuple {y_1, y_2} \iff \tuple {x_1 \prec_1 y_1} \lor \paren {x_1 = y_1 \land x_2 \preceq_2 y_2}$

## Pages in category "Lexicographic Order"

The following 8 pages are in this category, out of 8 total.

### L

- Lexicographic Order forms Well-Ordering on Ordered Pairs of Ordinals
- Lexicographic Order Initial Segments
- Lexicographic Order is Ordering
- Lexicographic Order on Pair of Well-Ordered Sets is Well-Ordering
- Lexicographic Order on Products of Well-Ordered Sets
- Lexicographic Order on Totally Ordered Sets is Total Ordering