抽象数学

数

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.]

The more abstract . . . we are from the body.
--Norris.

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.

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.

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.

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

{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}.