Definition of "inverse"

inverse

/ɪnˈvɝs/

adjective
not comparable
1. Opposite in effect, nature or order.
2. Reverse, opposite in order.
3. (botany) Inverted; having a position or mode of attachment the reverse of that which is usual.
4. (mathematics) 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.
5. (geometry) That has the property of being an inverse (the result of a circle inversion of a given point or geometrical figure); that is constructed by circle inversion.
6. (category theory, of a category) Whose every element has an inverse (morphism which is both a left inverse and a right inverse).
noun
plural inverses
1. (properly) upside down or (loosely) inside out or backwards.
2. The result of an inversion, particularly:
  1. The reverse of any procedure or process.
  2. (mathematics) A ratio etc. in which the antecedents and consequents are switched.
  3. (geometry) The result of a circle inversion; the set of all such points; the curve described by such a set.
  4. (logic) The non-truth-preserving proposition constructed by negating both the premise and conclusion of an initially given proposition.
    Quotations
    Inversion is the inferring, from a given proposition, another proposition whose subject is the contradictory of the subject of the original proposition. The given proposition is called the Invertend, that which is inferred from it is termed the Inverse... The rule for Inversion is: Convert either the Obverted Converse or the Obverted Contrapositive.
    1896, James Welton, A Manual of Logic, 2nd edition, Bk iii, Ch. iii, §102
3. (mathematics) A second element which negates a first; in a binary operation, the element for which the binary operation—when applied to both it and an initially given element—yields the operation's identity element, specifically:
  1. (addition) The negative of a given number.
  2. (multiplication) One divided by a given number.
  3. (functions) A second function which, when combined with the initially given function, yields as its output any term inputted into the first function.
4. (category theory) A morphism which is both a left inverse and a right inverse.
5. (card games) The winning of the coup in a game of rouge et noir by a card of a color different from that first dealt; the area of the table reserved for bets upon such an outcome.
  Quotations
  If the player... be determined to try his luck on the inverse, he must place his money on a yellow circle, or rather a collection of circles, situated at the extremity of the table.
  1850, Henry George Bohn, The Hand-book of Games, page 343
  The tailleur never mentions the words ‘Black’ or ‘Inverse’, but always says that Red wins or Red loses, and that the colour wins or the colour loses.
  1950, Lawrence Hawkins Dawson, Hoyle's Games Modernized, 20th edition, page 291
6. (linguistics, Kiowa-Tanoan) A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.
verb
third-person singular simple present inverses, present participle inversing, simple past and past participle inversed
1. (surveying) To compute the bearing and distance between two points.