纯粹数学
纯数学

[ noun ]
the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
<noun.cognition>

Pure \Pure\, a. [Compar. {Purer}; superl. {Purest}.] [OE. pur,
F. pur, fr. L. purus; akin to putus pure, clear, putare to
clean, trim, prune, set in order, settle, reckon, consider,
think, Skr. p? to clean, and perh. E. fire. Cf. {Putative}.]
1. Separate from all heterogeneous or extraneous matter; free
from mixture or combination; clean; mere; simple; unmixed;
as, pure water; pure clay; pure air; pure compassion.

The pure fetters on his shins great. --Chaucer.

A guinea is pure gold if it has in it no alloy. --I.
Watts.

2. Free from moral defilement or quilt; hence, innocent;
guileless; chaste; -- applied to persons. ``Keep thyself
pure.'' --1 Tim. v. 22.

Now the end of the commandment is charity out of a
pure heart, and of a good conscience. --1 Tim. i. 5.

3. Free from that which harms, vitiates, weakens, or
pollutes; genuine; real; perfect; -- applied to things and
actions. ``Pure religion and impartial laws.'' --Tickell.
``The pure, fine talk of Rome.'' --Ascham.

Such was the origin of a friendship as warm and pure
as any that ancient or modern history records.
--Macaulay.

4. (Script.) Ritually clean; fitted for holy services.

Thou shalt set them in two rows, six on a row, upon
the pure table before the Lord. --Lev. xxiv.
6.

5. (Phonetics) Of a single, simple sound or tone; -- said of
some vowels and the unaspirated consonants.

{Pure-impure}, completely or totally impure. ``The
inhabitants were pure-impure pagans.'' --Fuller.

{Pure blue}. (Chem.) See {Methylene blue}, under {Methylene}.


{Pure chemistry}. See under {Chemistry}.

{Pure mathematics}, that portion of mathematics which treats
of the principles of the science, or contradistinction to
applied mathematics, which treats of the application of
the principles to the investigation of other branches of
knowledge, or to the practical wants of life. See
{Mathematics}. --Davies & Peck (Math. Dict. )

{Pure villenage} (Feudal Law), a tenure of lands by uncertain
services at the will of the lord. --Blackstone.

Syn: Unmixed; clear; simple; real; true; genuine;
unadulterated; uncorrupted; unsullied; untarnished;
unstained; stainless; clean; fair; unspotted; spotless;
incorrupt; chaste; unpolluted; undefiled; immaculate;
innocent; guiltless; guileless; holy.


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}.