In
mathematics, a
directed set is a set equipped with a
transitive,
reflexive relation under which each pair of elements is bounded above. In other words, a set
A equipped with such a
relation--call it "≤"--is directed if whenever
x and
y are in
A there exists an element
z of
A which satisfies both
x ≤
z and
y ≤
z.
For example, the set of finite sets of integers, equipped with the partial order given by set inclusion, is directed: if X and Y are finite sets of integers, then their union Z is another finite set which contains each of them.