| 释义 |
associative, a.|əˈsəʊʃɪətɪv|
[f. L. associāt- (see associate) + -ive, as if ad. L. *associātīvus.]
1. Of, pertaining to, or characterized by association.
1881Rae in Contemp. Rev. Feb. 233 The associative principle in the arrangements of economical life.
2. Psychol. Of, pertaining to, characterized by, or subserving, the association of ideas. (Cf. association 7.)
1812Coleridge in Omniana II. 13 The fancy, or the aggregative and associative power. 1864J. S. Mill Lett. (1910) II. 7 He [sc. Spencer] has a great mastery over the obscurer applications of the associative principle. a1873― Three Ess. Relig. (1874) 199 When analysed to the bottom on the principles of the Associative Psychology, the brain..is, like matter itself, merely a set of human sensations either actual or inferred as possible. 1923J. S. Huxley Ess. of Biologist i. 24 Through associative memory, present behaviour is modified by past experience. 1957New Biol. XXIV. 123 Associative learning—a term which covers both classical conditioned reflexes and learning by trial and error.
3. Math. Governed by or stating the condition that where three or more quantities are connected together by operators, the result is independent of the grouping of the quantities as long as their order is unchanged, e.g. that (a×b)×c = a×(b×c).
1844W. R. Hamilton in Proc. R. Irish Acad. II. 430 It will be found that another important property of the old multiplication is preserved, or extended to the new, namely, that which may be called the associative character of the operation, and which may have for its type the formula Q. QI QII. QIII, QIV = QQI. QII QIII QIV. 1870B. Pierce Linear Associative Algebra 21 The associative principle of multiplication may be adopted, namely that the product of successive multiplications is not affected by the order in which the multiplications are performed, provided that there is no change in the relative position of the factors... This is quite an important limitation, and the algebras which are subject to it will be called associative. 1924[see Boolean a.]. 1964N. N. Hancock Matrix Analysis Electr. Machinery ii. 7 There may be more than two matrices in a product and in such cases matrix multiplication is associative. 1975I. Stewart Concepts Mod. Math. v. 73 We say that our method of combining functions satisfies the associative law.
Hence aˈssociatively adv.; associaˈtivity, † associativeness Math. the property of being associative.
1878Amer. Jrnl. Math. I. 50 The associativeness of such symbols arises from the circumstance that the definitions of α, β, γ,..determine the meanings of αβ, αγ, &c. 1880Cyples Hum. Exp. v. 110 So as to represent associatively. 1926Trans. Amer. Math. Soc. XXVIII. 222 The present direct method of finding the conditions for associativity is far more complicated than our earlier direct method. 1965J. J. Rotman Theory of Groups i. 4 Must we postulate more intricate associativity axioms in order to do without parentheses? 1979D. R. Hofstadter Gödel, Escher, Bach (1980) ii. 56 The commutativity and associativity of multiplication. |