Category:Lexicographic Order

From ProofWiki
Jump to navigation Jump to search

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:

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