lattice,
n. 1. an algebra endowed with two binary operations, denoted ^ and v, often called meet and join, that are symmetrical and associative, and for which
x ^ x = x = x v x
and
x ^ (x v y) = x = x v (x ^ y).
For example, the supremum and the infimum of a pair of functions define a lattice, as do the intersection and the union of subsets of a set. See upper bound, lower bound. See also Boolean algebra, partial ordering, integer lattice. 2. a partially ordered set in which each pair of elements has a supremum and an infimum.
x ^ x = x = x v x
and
x ^ (x v y) = x = x v (x ^ y).
For example, the supremum and the infimum of a pair of functions define a lattice, as do the intersection and the union of subsets of a set. See upper bound, lower bound. See also Boolean algebra, partial ordering, integer lattice. 2. a partially ordered set in which each pair of elements has a supremum and an infimum.