In many contexts in mathematics the term inverse indicates the opposite of something. This word and its derivatives are used widely in mathematics, as illustrated below.

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  1. The opposite of a given, due to contrary nature or effect.
    ''Deposing is the opposite of installing, and vice versa
  2. The reverse version of a procedure.
    Removing one's shoes is the inverse of putting one's shoes on
  3. The inverse of an element x with respect to a binary operation is an element that when combined with x yields the appropriate identity element.
    The additive inverse of x is -x as, x + -x = 0 where 0 is the additive identity element.
    The multiplicative inverse of x is x-1 as, x * x-1 = 1 where 1 is the multiplicative identity element.
    ''The compositional inverse of a function f is f–1 as, f f–1 is the identity function (ie f–1(f(a)) = a for all a).
  4. A statement constructed from the negatives of the premise and conclusion of some other statement: ~p → ~q is the inverse of p → q.


  1. To compute the bearing and distance between two points.


  1. Opposite in effect or nature or order
  2. reverse, opposite in order
  3. Inverted; having a position or mode of attachment the reverse of that which is usual.
  4. Having the properties of an inverse; said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity.
    Multiplication is the inverse operation to division.
  5. A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

The above text is a snippet from Wiktionary: inverse
and as such is available under the Creative Commons Attribution/Share-Alike License.

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