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Pure mathematics

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.

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.

Pure 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.] 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 or Pure mathematics. See 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.] 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 or Pure mathematics. See Mathematics.

- Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world...

- to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake)...

- Synopsis of Pure Mathematics is a book by G. S. Carr, written in 1886. The book attempted to summarize the state of most of the basic mathematics known at...

- subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected...

- A Course of Pure Mathematics is a cl****ic textbook in introductory mathematical analysis, written by G. H. Hardy. It is recommended for people studying...

- Symposia in Applied Mathematics Proceedings of Symposia in Pure Mathematics Blogs: Blog on Math Blogs e-Mentoring Network in the Mathematical Sciences AMS Graduate...

- Professorship of Pure Mathematics (originally in the statutes and for the first two professors, Sadlerian) is a professorship in pure mathematics within the...

- The Faculty of Mathematics at the University of Cambridge comprises the Department of Pure Mathematics and Mathematical Statistics (DPMMS) and the Department...

- m**** of the observable universe by a factor of roughly 7 x 1039. In pure mathematics, there are several notational methods for representing large numbers...

- in logic See also Areas of mathematics and Glossary of areas of mathematics. As a rough guide this list is divided into pure and applied sections although...

- to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake)...

- Synopsis of Pure Mathematics is a book by G. S. Carr, written in 1886. The book attempted to summarize the state of most of the basic mathematics known at...

- subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected...

- A Course of Pure Mathematics is a cl****ic textbook in introductory mathematical analysis, written by G. H. Hardy. It is recommended for people studying...

- Symposia in Applied Mathematics Proceedings of Symposia in Pure Mathematics Blogs: Blog on Math Blogs e-Mentoring Network in the Mathematical Sciences AMS Graduate...

- Professorship of Pure Mathematics (originally in the statutes and for the first two professors, Sadlerian) is a professorship in pure mathematics within the...

- The Faculty of Mathematics at the University of Cambridge comprises the Department of Pure Mathematics and Mathematical Statistics (DPMMS) and the Department...

- m**** of the observable universe by a factor of roughly 7 x 1039. In pure mathematics, there are several notational methods for representing large numbers...

- in logic See also Areas of mathematics and Glossary of areas of mathematics. As a rough guide this list is divided into pure and applied sections although...

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