n. 1a. intuitively, the class of all things that are not members of a given set. Because it is not relative to a universe, however, this attempted definition is too all-inclusive, and so gives rise to the contradictions of Russell's paradox and Cantor's paradox.
b. properly, the class of all members of a given universe of discourse that are not members of a given class, often written C(A) or A', where A is the given set. For example, if some given universal set is represented by the rectangle U in then the shaded region S' is the complement of the unshaded region S (and vice versa).
c. more generally, the relative complement of one set in another; the complement of a set in the preceding sense is its complement in the understood universal set. 2. the difference between some given value and a fixed total value, especially in complementary angle of a given angle. 3. (in a vector space) a subspace disjoint from a given subspace that when added to it gives the whole space. 4. in general, any element of a structure that is complementary to a given element, such as orthogonal vectors or elements in a lattice of which the meet is zero.