equivalencen.

/iːˈkwɪvələns/

Forms: Also 1600s æquivalence.

Etymology: < French équivalence, < medieval Latin aequivalentia , < aequivalent-em equivalent adj. and n.

a. The condition of being equivalent; equality of value, force, importance, significance, etc.

ΘΚΠ

the world > relative properties > relationship > equality or equivalence > [noun]

comparison1340

evennessa1398

evenhead?a1400

equipollencec1430

pareil?c1450

equalityc1460

comparation1483

egalness1526

equalness1530

equivalency1535

eveningc1540

equivalencea1542

indifferency1569

owelty1579

coequality1583

mateship1593

equal1596

adequation1605

parity1609

parility1610

matchableness1611

equipollency1623

equiparance1624

egality1628

equipage1633

comparitya1635

omniparity1635

peership1641

exequation1656

equipoise1658

equipotency1658

countervalue1660

adequateness1664

commensurablenessa1676

peerage1681

égalité1794

peerdom1891

a1542 T. Wyatt Psalm cxxx. Prol. 650 in Coll. Poems (1969) When he weyth the fawlt and recompense He..fyndyth playne A twene them to no whitt equivalence.

a1592 R. Greene Frier Bacon (1594) sig. G3^v Haue you courted and found Castile fit, To answer England in equiuolence [printed equinolence].

1652 J. Wadsworth tr. P. de Sandoval Civil Wars Spain 212 In satisfaction or equivalence thereof, hee might allow a pension or stipend to, etc.

1660 T. Stanley Hist. Philos. III. iv. 8 Æquivalence we call an equality as to belief or unbelief.

a1676 M. Hale Primitive Originat. Mankind (1677) i. ii. 53 No Organs..which are wanting in the constitution of the humane Body, at least in substance and equivalence.

1690 J. Norris Christian Blessedness 212 Tho there be no Proportion of Equivalence between our best Works and the Rewards of Heaven.

1867 G. H. Lewes Hist. Philos. (ed. 3) I. Prolegomena iii. p. lxiii The whole stress of Verification consists in reducing propositions to identity or equivalence.

1870 F. C. Bowen Logic viii. 250 It brings to light very clearly the virtual equivalence of those moods in the several Figures.

1890 Times 4 Jan. 9/2 Gold and silver will..assume equivalence at the ratio the Act names.

b. Physics. Equality of energy or effect.

ΚΠ

1874 W. R. Grove On Correlation Physical Forces (ed. 6) 61 The relation is not a relation of simple mechanical equivalence.

1878 B. Stewart & P. G. Tait Unseen Universe 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 n. the doctrine that force of one kind becomes transformed into force of another kind of the same value. Cf. conservation of energy at conservation n. 3.

ΚΠ

1867 Macmillan's Mag. Sept. 372/1 The doctrine called the Correlation, Persistence, Equivalence, Transmutability, Indestructibility of Force.

1879 J. Tyndall Fragm. Sci. (ed. 6) II. xiv. 348 No engine..can evade this law of equivalence, or perform on its own account the smallest modicum of work.

d. principle of equivalence n. (also equivalence principle) 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.The principle was proposed by Einstein in Ann. d. Physik (1911) XXXV. 898–908, and was first called äquivalenzprinzip by him in Ann. d. Physik (1912) XXXVIII. 360, 443.

ΚΠ

1918 A. 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.

1955 O. Klein in W. Pauli Niels Bohr & Devel. Physics 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. Chemistry. The doctrine that differing fixed quantities of different substances are ‘equivalent’ in chemical combinations.

ΚΠ

1880 tr. Wurtz' Atom. Th. 76 He mentions polybasic acids as forming an exception to the theory of equivalence.

Draft additions 1993

3. An instance of equivalence, in various senses (esp. in Mathematics and Linguistics).

ΘΚΠ

the world > relative properties > relationship > equality or equivalence > [noun] > equal, counterpart, or equivalent > specific types of

equipollencec1400

equipollency1652

par1709

isopsephism1882

equivalence1906

equivalency1961

1906 B. Russell in Amer. Jrnl. Math. 28 198 Thus both p and not-p may be replaced, in implicational formulae, by equivalences.

1960 E. 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 C. Lévi-Strauss in P. Maranda Mythology xiii. 275 They are operators, which make it possible..to express..a set of equivalences connecting life and death, vegetable foods and cannibalism, putrefaction and imputrescibility, [etc.].

Draft additions 1993

4. Compounds.

equivalence class n. Mathematics a class of all the elements of a set which are equivalent to one another in terms of a given equivalence relation.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of

interval1838

identity1894

identity element1902

complement1937

supremum1938

infimum1940

sup1940

equivalence class1952

1948 W. 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’.]

1952 S. C. Kleene Introd. Metamath. i. 9 Von Neumann 1928 chooses from each of these sets of sets (‘equivalence classes’ [Ger. Äquivalenzklassen]) a particular set to serve as the cardinal of any set in the class.

1982 W. 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 n. Mathematics a relation between elements of a set that is reflexive, symmetric, and transitive.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of > relation between

well-ordering1914

symmetric difference1936

partial ordering1938

equivalence relation1940

symmetrical difference1978

1940 E. T. Bell Devel. Math. ix. 177 A relation such as ∼ is called an ‘equivalence relation’ for the given class.

1959 E. M. Patterson Topology (ed. 2) ii. 21 Congruence and similarity in Euclidean geometry..are..equivalence relations.

1963 G. 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 A. J. Jones Game Theory iv. 194 To prove the theorem it is only necessary to verify the three defining properties of an equivalence relation... Reflexivity... Symmetry... Transitivity.

This entry has not yet been fully updated (first published 1891; most recently modified version published online June 2021).

单词	equivalence
释义	equivalencen. /iːˈkwɪvələns/ Forms: Also 1600s æquivalence. Etymology: < French équivalence, < medieval Latin aequivalentia , < aequivalent-em equivalent adj. and n. 1. a. The condition of being equivalent; equality of value, force, importance, significance, etc. ΘΚΠ the world > relative properties > relationship > equality or equivalence > [noun] comparison1340 evennessa1398 evenhead?a1400 equipollencec1430 pareil?c1450 equalityc1460 comparation1483 egalness1526 equalness1530 equivalency1535 eveningc1540 equivalencea1542 indifferency1569 owelty1579 coequality1583 mateship1593 equal1596 adequation1605 parity1609 parility1610 matchableness1611 equipollency1623 equiparance1624 egality1628 equipage1633 comparitya1635 omniparity1635 peership1641 exequation1656 equipoise1658 equipotency1658 countervalue1660 adequateness1664 commensurablenessa1676 peerage1681 égalité1794 peerdom1891 a1542 T. Wyatt Psalm cxxx. Prol. 650 in Coll. Poems (1969) When he weyth the fawlt and recompense He..fyndyth playne A twene them to no whitt equivalence. a1592 R. Greene Frier Bacon (1594) sig. G3^v Haue you courted and found Castile fit, To answer England in equiuolence [printed equinolence]. 1652 J. Wadsworth tr. P. de Sandoval Civil Wars Spain 212 In satisfaction or equivalence thereof, hee might allow a pension or stipend to, etc. 1660 T. Stanley Hist. Philos. III. iv. 8 Æquivalence we call an equality as to belief or unbelief. a1676 M. Hale Primitive Originat. Mankind (1677) i. ii. 53 No Organs..which are wanting in the constitution of the humane Body, at least in substance and equivalence. 1690 J. Norris Christian Blessedness 212 Tho there be no Proportion of Equivalence between our best Works and the Rewards of Heaven. 1867 G. H. Lewes Hist. Philos. (ed. 3) I. Prolegomena iii. p. lxiii The whole stress of Verification consists in reducing propositions to identity or equivalence. 1870 F. C. Bowen Logic viii. 250 It brings to light very clearly the virtual equivalence of those moods in the several Figures. 1890 Times 4 Jan. 9/2 Gold and silver will..assume equivalence at the ratio the Act names. b. Physics. Equality of energy or effect. ΚΠ 1874 W. R. Grove On Correlation Physical Forces (ed. 6) 61 The relation is not a relation of simple mechanical equivalence. 1878 B. Stewart & P. G. Tait Unseen Universe 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 n. the doctrine that force of one kind becomes transformed into force of another kind of the same value. Cf. conservation of energy at conservation n. 3. ΚΠ 1867 Macmillan's Mag. Sept. 372/1 The doctrine called the Correlation, Persistence, Equivalence, Transmutability, Indestructibility of Force. 1879 J. Tyndall Fragm. Sci. (ed. 6) II. xiv. 348 No engine..can evade this law of equivalence, or perform on its own account the smallest modicum of work. d. principle of equivalence n. (also equivalence principle) 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.The principle was proposed by Einstein in Ann. d. Physik (1911) XXXV. 898–908, and was first called äquivalenzprinzip by him in Ann. d. Physik (1912) XXXVIII. 360, 443. ΚΠ 1918 A. 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. 1955 O. Klein in W. Pauli Niels Bohr & Devel. Physics 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. Chemistry. The doctrine that differing fixed quantities of different substances are ‘equivalent’ in chemical combinations. ΚΠ 1880 tr. Wurtz' Atom. Th. 76 He mentions polybasic acids as forming an exception to the theory of equivalence. Draft additions 1993 3. An instance of equivalence, in various senses (esp. in Mathematics and Linguistics). ΘΚΠ the world > relative properties > relationship > equality or equivalence > [noun] > equal, counterpart, or equivalent > specific types of equipollencec1400 equipollency1652 par1709 isopsephism1882 equivalence1906 equivalency1961 1906 B. Russell in Amer. Jrnl. Math. 28 198 Thus both p and not-p may be replaced, in implicational formulae, by equivalences. 1960 E. 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 C. Lévi-Strauss in P. Maranda Mythology xiii. 275 They are operators, which make it possible..to express..a set of equivalences connecting life and death, vegetable foods and cannibalism, putrefaction and imputrescibility, [etc.]. Draft additions 1993 4. Compounds. equivalence class n. Mathematics a class of all the elements of a set which are equivalent to one another in terms of a given equivalence relation. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of interval1838 identity1894 identity element1902 complement1937 supremum1938 infimum1940 sup1940 equivalence class1952 1948 W. 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’.] 1952 S. C. Kleene Introd. Metamath. i. 9 Von Neumann 1928 chooses from each of these sets of sets (‘equivalence classes’ [Ger. Äquivalenzklassen]) a particular set to serve as the cardinal of any set in the class. 1982 W. 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 n. Mathematics a relation between elements of a set that is reflexive, symmetric, and transitive. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of > relation between well-ordering1914 symmetric difference1936 partial ordering1938 equivalence relation1940 symmetrical difference1978 1940 E. T. Bell Devel. Math. ix. 177 A relation such as ∼ is called an ‘equivalence relation’ for the given class. 1959 E. M. Patterson Topology (ed. 2) ii. 21 Congruence and similarity in Euclidean geometry..are..equivalence relations. 1963 G. 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 A. J. Jones Game Theory iv. 194 To prove the theorem it is only necessary to verify the three defining properties of an equivalence relation... Reflexivity... Symmetry... Transitivity. This entry has not yet been fully updated (first published 1891; most recently modified version published online June 2021). † equivalencev. Etymology: < equivalence n. transitive. To balance, serve as equipoise to.Apparently an isolated use. ΘΚΠ the world > relative properties > relationship > equality or equivalence > make equal [verb (transitive)] > be equivalent to quitc1375 countervailc1380 containa1387 value1561 to go for ——1574 countervalue1581 weigh1583 avail1598 reanswer1598 commeasure1615 imply1634 equivalence1646 equivale1659 1646 Sir T. Browne Pseudodoxia Epidemica i. i. 3 Whether the resistibility of his reason did not equivalence the facility of her seduction. View more context for this quotation This entry has not yet been fully updated (first published 1891; most recently modified version published online March 2021). < n.a1542v.1646
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equivalencen.

Draft additions 1993

Draft additions 1993

† equivalencev.