Category:Definitions/Lexicographic Order
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This category contains definitions related to Lexicographic Order.
Related results can be found in Category:Lexicographic Order.
Let $\struct {S_1, \preccurlyeq_1}$ and $\struct {S_2, \preccurlyeq_2}$ be ordered sets.
The lexicographic order $\struct {S_1, \preccurlyeq_1} \otimes^l \struct {S_2, \preccurlyeq_2}$ on $\struct {S_1, \preccurlyeq_1}$ and $\struct {S_2, \preccurlyeq_2}$ is the ordered set $\struct {T, \preccurlyeq_l}$ where:
- $T := S_1 \times S_2$, that is, the Cartesian product of $S_1$ and $S_2$
- $\preccurlyeq_l$ is the relation defined on $T$ as:
- $\tuple {x_1, x_2} \preccurlyeq_l \tuple {y_1, y_2} \iff \tuple {x_1 \prec_1 y_1} \lor \paren {x_1 = y_1 \land x_2 \preccurlyeq_2 y_2}$
Pages in category "Definitions/Lexicographic Order"
The following 9 pages are in this category, out of 9 total.
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- Definition:Lexicographic Order
- Definition:Lexicographic Order on Family
- Definition:Lexicographic Order/Also known as
- Definition:Lexicographic Order/Family
- Definition:Lexicographic Order/General Definition
- Definition:Lexicographic Order/Ordinals
- Definition:Lexicographic Order/Tuples of Equal Length
- Definition:Lexicographic Order/Tuples of Equal Length/Cartesian Space
- Definition:Lexicographic Ordering