Definition: arbitrary

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Source: WordNet (r) 1.7 

arbitrary
     adj : based on or subject to individual discretion or preference
           or sometimes impulse or caprice; "an arbitrary
           decision"; "the arbitrary rule of a dictator";"an
           arbitrary penalty"; "of arbitrary size and shape"; "an
           arbitrary choice"; "arbitrary division of the group
           into halves" [ant: nonarbitrary]

Source: Webster's Revised Unabridged Dictionary (1913) 

Arbitrary \Ar"bi*tra*ry\, a. [L. arbitrarius, fr. arbiter: cf.
   F. arbitraire. See Arbiter.]
   1. Depending on will or discretion; not governed by any fixed
      rules; as, an arbitrary decision; an arbitrary punishment.

            It was wholly arbitrary in them to do so. --Jer.
                                                  Taylor.

            Rank pretends to fix the value of every one, and is
            the most arbitrary of all things.     --Landor.

   2. Exercised according to one's own will or caprice, and
      therefore conveying a notion of a tendency to abuse the
      possession of power.

            Arbitrary power is most easily established on the
            ruins of liberty abused licentiousness.
                                                  --Washington.

   3. Despotic; absolute in power; bound by no law; harsh and
      unforbearing; tyrannical; as, an arbitrary prince or
      government.                                 --Dryden.

   Arbitrary constant, Arbitrary function (Math.), a
      quantity of function that is introduced into the solution
      of a problem, and to which any value or form may at will
      be given, so that the solution may be made to meet special
      requirements.

   Arbitrary quantity (Math.), one to which any value can be
      assigned at pleasure.