Abstract mathematics

Abstract mathematics
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.] [1913 Webster]

The more abstract . . . we are from the body. --Norris. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

4. Abstracted; absent in mind. ``Abstract, as in a trance.'' --Milton. [1913 Webster]

{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}. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • 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.] [1913 Webster] The more abstract . . . we are from the body. Norris. [1913 Webster] 2.… …   The Collaborative International Dictionary of English

  • 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.] [1913 Webster] The more abstract . . . we are from the body. Norris. [1913 Webster] …   The Collaborative International Dictionary of English

  • Abstract terms — 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.] [1913 Webster] The more abstract . . . we are from the body. Norris. [1913 Webster] …   The Collaborative International Dictionary of English

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  • Mathematics — Math e*mat ics, n. [F. math[ e]matiques, pl., L. mathematica, sing., Gr. ? (sc. ?) science. See {Mathematic}, and { ics}.] That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of… …   The Collaborative International Dictionary of English

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