complement

<logic>

1. The other value or values in the set of possible values.

See logical complement, bitwise complement, set complement.

[FOLDOC]

2. complement of a set

<logic> The complement of a set A is the set of elements that are not members of A. Notation: A with a single bar over the top, or -A, or A'.

a. Absolute complement of a set

The set of all things whatsoever that are not members of the given set. Standard set theory does not recognize absolute complements. See Russell's paradox

b. Relative complement of a set

The set of all things that are not members of the given set, A, but that are members of some particular "background" set, B. This can be expressed through the notation for set difference: the relative complement of A in B or relative to B (A against the background of B) is the set x : (x : B) o. The background set is sometimes called the universe or universe of discourse. Notation: B-A, or B\A.

[Glossary of First-Order Logic]

<2001-03-16>

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Nearby terms: compatibilism « compatibility « compatible « complement » complementary non-deterministic polynomial » complete » complete graph