| 释义 |
▪ I. equivalence, n.|iːˈkwɪvələns|
Also 7 æquivalence.
[a. F. équivalence, ad. med.L. æquivalentia, f. æquivalent-em equivalent.]
1. a. The condition of being equivalent; equality of value, force, importance, significance, etc.
a1541Wyatt Poet. Wks. (1861) 203 When he weigheth the fault and recompense, He..findeth plain Atween them two no whit equivalence. 1590Greene Fr. Bacon Wks. (ed. Dyce) 173/2 Have you courted and found Castile fit To answer England in equivalence? 1652Wadsworth tr. Sandoval's Civ. Wars Spain 212 In satisfaction or equivalence thereof, hee might allow a pension or stipend to, etc. 1655–60Stanley Hist. Philos. (1701) 467/1 æquivalence we call an equality as to Belief or Unbelief. 1677Hale Prim. Orig. Man. i. ii. 53 No Organs..which are wanting in the constitution of the humane Body, at least in substance and equivalence. 1690Norris Beatitudes (1694) I. 214 Tho there be no Proportion of Equivalence between our best Works and the Rewards of Heaven. 1847Lewes Hist. Philos. (1867) I. Introd. 63 The whole stress of Verification consists in reducing propositions to identity or equivalence. 1870Bowen Logic viii. 250 It brings to light very clearly the virtual equivalence of those moods in the several Figures. 1890Times 4 Jan. 9/2 Gold and silver will..assume equivalence at the ratio the Act names.
b. Physics. Equality of energy or effect.
1842Grove Corr. Phys. Forces (ed. 6) 61 The relation is not a relation of simple mechanical equivalence. 1878Tait & Stewart Unseen Univ. iii. 112 But the exact and formal enuntiation of the equivalence of heat and work..was given by Davy in 1812.
c. equivalence of force: the doctrine that force of one kind becomes transformed into force of another kind of the same value. Cf. conservation of energy, energy 6.
1871Tyndall Fragm. Sc. (ed. 6) II. xiv. 348 No engine..can evade this law of equivalence, or perform on its own account the smallest modicum of work. 1863B. Stewart Conserv. Force viii. 205 The doctrine called the correlation, persistence, equivalence, transmutability, indestructibility of force.
d. principle of equivalence: one of the fundamental postulates of the general theory of relativity, which states that at any point of space-time the effects of a gravitational field cannot be experimentally distinguished from those due to an accelerated frame of reference. Also equivalence principle.
The principle was proposed by Einstein in Ann. d. Physik (1911) XXXV. 898–908, and was first called äquivalenzprinzip by him in Ibid. (1912) XXXVIII. 360, 443.
1918A. S. Eddington Rep. Relativity Theory Gravitation ii. 19 The hypothesis that gravitation may be of essentially the same nature as the geometrical forces introduced by the choice of co-ordinates..which was put forward by Einstein, is called the Principle of Equivalence. 1955O. Klein in W. Pauli Niels Bohr 99 In a generalized quantum-relativity theory, comprising also electromagnetism and perhaps meson fields corresponding to the nuclear forces, there would probably be some kind of generalized equivalence principle.
2. Chem. The doctrine that differing fixed quantities of different substances are ‘equivalent’ in chemical combinations.
1880tr. Wurtz' Atom. Th. 76 He mentions polybasic acids as forming an exception to the theory of equivalence.
Add:3. An instance of equivalence, in various senses (esp. in Math. and Linguistics).
1906B. Russell in Amer. Jrnl. Math. XXVIII. 198 Thus both p and not-p may be replaced, in implicational formulae, by equivalences. 1960E. H. Gombrich Art & Illusion x. 345 All artistic discoveries are discoveries not of likenesses but of equivalences which enable us to see reality in terms of an image and an image in terms of reality. 1972[see imputrescibility n.].
4. Special comb.: equivalence class Math., a class of all the elements of a set which are equivalent to one another in terms of a given equivalence relation.
[1948W. H. Werkmeister Basis & Struct. of Knowl. vi. 205 No matter how much the elements of these various classes differ in quality, the classes themselves, as equivalent classes, have something in common—something which is ‘invariant’ and which constitutes their ‘equivalence’.] 1952S. C. Kleene Introd. Metamath. i. 9 Von Neumann 1928 chooses from each of these sets of sets (‘*equivalence classes’ [G. Äquivalenzklassen]) a particular set to serve as the cardinal of any set in the class. 1982W. S. Hatcher Logical Found. Math. iii. 89 The integers can be introduced as equivalence classes of ordered pairs of natural numbers, and the rational numbers as certain equivalence classes of ordered pairs of integers.
equivalence relation Math., a relation between elements of a set that is reflexive, symmetric, and transitive.
1940E. T. Bell Devel. Math. ix. 177 A relation such as ∼ is called an ‘equivalence relation’ for the given class. 1959E. M. Patterson Topology (ed. 2) ii. 21 Congruence and similarity in Euclidean geometry..are..equivalence relations. 1963G. F. Simmons Introd. Topol. & Mod. Anal. i. 27 If we start with a partition, we get an equivalence relation by regarding elements as equivalent if they belong to the same partition set, and if we start with an equivalence relation, we get a partition by grouping together into subsets all elements which are equivalent to one another. 1980[see transitivity n.].
▪ II. † equivalence, v. nonce-wd.
[f. prec. n.]
trans. To balance, serve as equipoise to.
1646Sir T. Browne Pseud. Ep. i. i. 3 Whether the resistibility of his reason did not equivalence the facility of her seduction. |