单词 | associative |
释义 | associativeadj. 1. Of, pertaining to, or characterized by association. ΚΠ 1881 Rae in Contemp. Rev. Feb. 233 The associative principle in the arrangements of economical life. 2. Psychology. Of, pertaining to, characterized by, or subserving, the association of ideas. (Cf. association n. 7.) ΘΚΠ the world > relative properties > relationship > accompaniment > [adjective] collateral1377 assistant1485 coincident1567 accompanying1600 concomitant1608 comitant1614 belonginga1616 concomitaneous1661 adjoint1727 associative1812 attended1846 herewith1917 the mind > mental capacity > psychology > psychology of ideas > association of ideas > [adjective] associative1812 1812 Coleridge in Omniana II. 13 The fancy, or the aggregative and associative power. 1864 J. S. Mill Lett. (1910) II. 7 He [sc. Spencer] has a great mastery over the obscurer applications of the associative principle. a1873 J. S. Mill 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. 1923 J. S. Huxley Ess. Biologist i. 24 Through associative memory, present behaviour is modified by past experience. 1957 New Biol. 24 123 Associative learning—a term which covers both classical conditioned reflexes and learning by trial and error. 3. Mathematics. 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). ΘΚΠ the world > relative properties > number > algebra > [adjective] > relating to expressions interscendent1796 symmetrical1816 zeta-ic1840 associative1844 discriminantal1852 symmetric1853 discriminant1870 idempotent1870 interscendental1873 bilinear1886 non-trivial1901 left1926 right1930 1844 W. R. Hamilton in Proc. Royal Irish Acad. 1840–4 2 430 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. 1870 B. 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 Trans. Amer. Math. Soc. 26 175 A commutative boolean operation which always has an inverse is also associative. 1964 N. N. Hancock Matrix Anal. Electr. Machinery ii. 7 There may be more than two matrices in a product and in such cases matrix multiplication is associative. 1975 I. Stewart Concepts Mod. Math. v. 73 We say that our method of combining functions satisfies the associative law. Derivatives aˈssociatively adv. ΘΚΠ the world > relative properties > relationship > accompaniment > [adverb] > together withc888 to-samec893 amongeOE togethersc1175 yferea1200 i-menec1200 togetherc1220 ymonec1300 i-samec1320 insamea1400 alongst with1582 jointly1656 concomitantly1696 collaterally1800 associatively1880 in tandem1930 in harness1967 1880 W. Cyples Inq. Proc. Human Exper. v. 110 So as to represent associatively. associaˈtivity n. ΘΚΠ the world > relative properties > number > algebra > [noun] > algebraic property associativeness1878 symmetry1888 associativity1926 idempotence1934 distributivity1940 idempotency1940 1926 Trans. Amer. Math. Soc. 28 222 The present direct method of finding the conditions for associativity is far more complicated than our earlier direct method. 1965 J. J. Rotman Theory of Groups i. 4 Must we postulate more intricate associativity axioms in order to do without parentheses? 1979 D. R. Hofstadter Gödel, Escher, Bach (1980) ii. 56 The commutativity and associativity of multiplication. ΘΚΠ the world > relative properties > number > algebra > [noun] > algebraic property associativeness1878 symmetry1888 associativity1926 idempotence1934 distributivity1940 idempotency1940 1878 Amer. Jrnl. Math. 1 50 The associativeness of such symbols arises from the circumstance that the definitions of α, β, γ,..determine the meanings of αβ, αγ, &c. This entry has not yet been fully updated (first published 1885; most recently modified version published online December 2021). < |
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