Abstract numbers

Abstract \Ab"stract`\ (#; 277), a. [L. abstractus, p. p. of
   abstrahere to draw from, separate; ab, abs + trahere to draw.
   See {Trace}.]
   1. Withdraw; separate. [Obs.]
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            The more abstract . . . we are from the body.
                                                  --Norris.
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   2. Considered apart from any application to a particular
      object; separated from matter; existing in the mind only;
      as, abstract truth, abstract numbers. Hence: ideal;
      abstruse; difficult.
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   3. (Logic)
      (a) Expressing a particular property of an object viewed
          apart from the other properties which constitute it;
          -- opposed to {concrete}; as, honesty is an abstract
          word. --J. S. Mill.
      (b) Resulting from the mental faculty of abstraction;
          general as opposed to particular; as, "reptile" is an
          abstract or general name. --Locke.
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                A concrete name is a name which stands for a
                thing; an abstract name which stands for an
                attribute of a thing. A practice has grown up in
                more modern times, which, if not introduced by
                Locke, has gained currency from his example, of
                applying the expression "abstract name" to all
                names which are the result of abstraction and
                generalization, and consequently to all general
                names, instead of confining it to the names of
                attributes.                       --J. S. Mill.
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   4. Abstracted; absent in mind. "Abstract, as in a trance."
      --Milton.
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   {An abstract idea} (Metaph.), an idea separated from a
      complex object, or from other ideas which naturally
      accompany it; as the solidity of marble when contemplated
      apart from its color or figure.

   {Abstract terms}, those which express abstract ideas, as
      beauty, whiteness, roundness, without regarding any object
      in which they exist; or abstract terms are the names of
      orders, genera or species of things, in which there is a
      combination of similar qualities.

   {Abstract numbers} (Math.), numbers used without application
      to things, as 6, 8, 10; but when applied to any thing, as
      6 feet, 10 men, they become concrete.

   {Abstract mathematics} or {Pure mathematics}. See
      {Mathematics}.
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