An ordering for the Cartesian product 
of any two sets 
and 
with order relations 
and 
, respectively, such that if 
and 
both belong to 
, then 
iff either
1. 
,
or
2. 
and 
.
The lexicographic order can be readily extended to cartesian products of arbitrary length by recursively applying this definition, i.e., by observing that 
.
When applied to permutations, lexicographic order is increasing numerical order (or equivalently, alphabetic order for lists of symbols;
Skiena 1990, p. 4). For example, the permutations
of 
in lexicographic order are 123, 132, 213, 231, 312, and 321.
When applied to subsets, two subsets are ordered by their smallest elements (Skiena 1990, p. 44). For example, the subsets of 
in lexicographic order are 
, 
, 
, 
, 
, 
, 
, 
.
Lexicographic order is sometimes called dictionary order.
