This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.
Complement
From Intelligent Perception
Given a set X and a subset A, the complement X \ A of A in X is "the rest of X":
X \ A = {x in X but not in A}.
Example.
R \ (0,1] = (-∞, 0] U (1, ∞).
In other words, a subset and its complement form a partition of the ambient set:
A U (X \ A) = X, and A ∩ (X \ A) = ∅.
In topology, complements of open sets are closed (see Open and closed sets) and vice versa.
Compare to orthogonal complement.
