# lexicographic order

**lexicographic order** The order of words in a dictionary, given the order of letters in the alphabet. In general, let a set *S* be well-ordered by relation <, and for *n *> 0 let *T* be a set of *n*-tuples (*x*_{1},*x*_{2},…,*x _{n}*)

of elements

*x*in

_{j}*S*. Then the ordering relation < over such

*n*-tuples can be defined so that (

*x*

_{1},…,

*x*) < (

_{n}*y*

_{1},…,

*y*)

_{n}iff

*x*

_{1}<

*y*

_{1}or there is some

*k*, 1 ←

*k*←

*n*, for which

*x*=

_{i}*y*for 1 ←

_{i}*i*<

*k*

*x*<

_{k}*y*

_{k}The set

*T*is in lexicographic order if the

*n*-tuples are sorted with respect to this relation. The concept can be extended to strings whose lengths may be different. The order would then be that in which words are placed in a dictionary.

#### More From encyclopedia.com

Domain , Domain
The domain of a relation is the set that contains all the first elements, x, from the ordered pairs (x,y) that make up the relation. In mathem… Inverse Matrix , Inverse Matrix
BIBLIOGRAPHY
The concept of inverse matrix is somewhat analogous to that of the reciprocal of a number. If a is a nonzero number, then… Garrett Birkhoff , Birkhoff was the son of mathematician George David Birkhoff and Margaret Grafius Birkhoff. George Birkhoff, the father, was the first American mathem… George Boole , Boole, George
Boole, George
(b. Lioncoln, England, 1815; d. Cork, Ireland, 1864)
mathematics.
George Boole was the son of John Boole, a cobbler whose… Inequality , In mathematics , an inequality is a statement about the relative order of members of a set. For instance, if S
is the set of positive integers , and… Diophantus Of Alexandria , Diophantus of Alexandria
Diophantus of Alexandria
(fl. ad. 250)
mathematics.
We know virtually nothing about the life of Diophantus. The dating of hi…

#### You Might Also Like

#### NEARBY TERMS

**lexicographic order**