Complement (mathematics) - Definition and Overview

The word complement (with an e in the second syllable, not to be confused with a different word, compliment with an i) has a number of uses. Generally a complement of X is something that together with X makes a complete whole; that supplies what X lacks. The first e in complete and the first e in complement are etymological cognates of each other in a way that is a useful mnemonic for remembering that this is not compliment with an i.

For various uses of this word in fields other than mathematics, see complement, a disambiguation page.

In mathematics, the word complement has a variety of uses. See:

• Complement (set theory)
• Complement (graph theory)
• Knot complement
• Orthogonal complement
• Schur complement
• An operation that transforms an integer into its additive inverse, useful for subtracting numbers when only addition is possible, or is easiest.
• Relatively complemented lattice
• Method of complements
  • Two's complement is often used in computer microprocessors which perform calculations using the binary numeral system.
  • One's complement
• Complementary angles
• Complement operator (regular expressions)

See Boolean algebra for an account of complements in that field.