[W/K] :: inverse

  Inverse \In*verse"\, a. [L. inversus, p. p. of invertere: cf. F.
     inverse. See Invert.]
     [1913 Webster]
     1. Opposite in order, relation, or effect; reversed;
        inverted; reciprocal; -- opposed to direct.
        [1913 Webster]
  
     2. (Bot.) Inverted; having a position or mode of attachment
        the reverse of that which is usual.
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     3. (Math.) Opposite in nature and effect; -- said with
        reference to any two operations, which, when both are
        performed in succession upon any quantity, reproduce that
        quantity; as, multiplication is the inverse operation to
        division. The symbol of an inverse operation is the symbol
        of the direct operation with -1 as an index. Thus sin-1 x
        means the arc or angle whose sine is x.
        [1913 Webster]
  
     Inverse figures (Geom.), two figures, such that each point
        of either figure is inverse to a corresponding point in
        the order figure.
  
     Inverse points (Geom.), two points lying on a line drawn
        from the center of a fixed circle or sphere, and so
        related that the product of their distances from the
        center of the circle or sphere is equal to the square of
        the radius.
  
     Inverse ratio, or Reciprocal ratio (Math.), the ratio of
        the reciprocals of two quantities.
  
     Inverse proportion, or Reciprocal proportion, an equality
        between a direct ratio and a reciprocal ratio; thus, 4 : 2
        : : 1/3 : 1/6, or 4 : 2 : : 3 : 6, inversely.
        [1913 Webster]

  Inverse \In"verse\, n.
     That which is inverse.
     [1913 Webster]
  
           Thus the course of human study is the inverse of the
           course of things in nature.              --Tatham.
     [1913 Webster]

  inverse
       adj 1: reversed (turned backward) in order or nature or effect
              [syn: reverse]
       2: opposite in nature or effect or relation to another quantity
          ; "a term is in inverse proportion to another term if it
          increases (or decreases) as the other decreases (or
          increases)" [ant: direct]
       n : something inverted in sequence or character or effect; "when
           the direct approach failed he tried the inverse" [syn: opposite]

  79 Moby Thesaurus words for "inverse":
     adversative, adverse, adversive, antagonistic, anti, antipathetic,
     antipodal, antipode, antipodes, antipole, antithesis, antithetic,
     antonym, antonymous, at cross-purposes, balancing, change,
     clashing, compensating, conflicting, confronting, contra,
     contradictory, contradistinct, contrapositive, contrarious,
     contrary, contrasted, converse, counter, counterbalance,
     counterbalancing, countercheck, counterpoint, counterpoise,
     counterpoised, counterpole, counterterm, countervailing,
     dead against, discordant, discrepant, eyeball to eyeball,
     eyeball-to-eyeball, facing, foil, heads, hostile, inconsistent,
     inimical, invert, obverse, offset, opposed, opposing, opposite,
     opposite number, opposite side, oppositional, oppositive,
     oppugnant, other face, other side, perverse, polar, polaric,
     polarized, repugnant, reverse, revert, setoff, squared off, tails,
     the contrary, the other side, transplace, transpose, turn,
     vis-a-vis
  
  

  inverse
       
           Given a function, f : D -> C, a function g : C
          -> D is called a left inverse for f if for all d in D, g (f d)
          = d and a right inverse if, for all c in C, f (g c) = c and an
          inverse if both conditions hold.  Only an injection has a
          left inverse, only a surjection has a right inverse and only
          a bijection has inverses.  The inverse of f is often written
          as f with a -1 superscript.
       
          (1996-03-12)