-adicsuffix

Primary stress is attracted to the first syllable of this suffix and vowels may be reduced accordingly, e.g. p-adic Brit.

/pɪˈadɪk/, U.S.

/piˈædɪk/.

Origin: Formed within English, by derivation. Etymons: -ad suffix¹, -ic suffix.

Etymology: < -ad suffix¹ + -ic suffix, after monadic adj., dyadic adj., polyadic adj., etc.

†1. Chemistry. With preceding symbol, designating an atom with a valency represented by the symbol. Cf. monadic adj. 3a, dyadic adj. b. Obsolete. rare.

ΚΠ

1878 Amer. Jrnl. Math. 1 83 In any compound an arbitrarily selected group of m n-adic atoms may be replaced by a group of n m-adic atoms.

2. Mathematics. With preceding symbol or numeral (esp. the generalized symbol p, denoting a prime number), forming adjectives designating numbers expressible as a sequence of digits in the base represented by the symbol (or as a power series in this quantity).

ΚΠ

1905 J. Pierpont Lect. Theory Functions Real Variables I. ii. 92 When m is used as base, the numbers a are said to be expressed in an m-adic system.

1921 Ann. Math. 23 84 The decadic integer ⋯,333,334 cannot be a 3-adic integer since the denominator of 2/3 is not prime to the base 3.

1939 Amer. Jrnl. Math. 61 894 In our case the ring of all p-adic integers o takes the place of the field of all real numbers.

1990 Proc. London Math. Soc. 60 37 (heading) Cell decomposition and local zeta functions in a tower of unramified extensions of a p-adic field.

2004 College Math. Jrnl. 35 323 Paul Monksky's elegant 1970 proof.., using Sperner's Lemma and 2-adic valuations.

3. Chiefly Mathematics and Logic. With preceding symbol (usually n), forming adjectives designating a function, operator, relation, etc., having the number of arguments represented by the given symbol. Cf. -ary suffix¹ Additions.

ΚΠ

1906 Proc. Amer. Philos. Soc. 45 99 There are relations dyadic, triadic, n-adic, there are relations symmetrical, unsymmetrical transitive, intransitive.

1940 W. V. Quine Math. Logic 225 A range of n-argument functionality..is itself an n-adic relation.

1975 Notre Dame Jrnl. Formal Logic 16 87 An arbitrary k-adic operator over X(n) defined by an expression with S as the sole operator.

1992 Mind 101 137 Fusion of n singletons to form a plural class is a complex type of conjunction which conjoins n monadic universals to form an n-adic relation.

2009 V. Anashin & A. Khrennikov Appl. Algebraic Dynamics viii. 257 All compositions of basic instructions, that is, computer programs, are uniformly continuous 2-adic functions.

This entry has been updated (OED Third Edition, December 2011; most recently modified version published online December 2021).

单词	-adic
释义	-adicsuffix Primary stress is attracted to the first syllable of this suffix and vowels may be reduced accordingly, e.g. p-adic Brit. /pɪˈadɪk/, U.S. /piˈædɪk/. Origin: Formed within English, by derivation. Etymons: -ad suffix¹, -ic suffix. Etymology: < -ad suffix¹ + -ic suffix, after monadic adj., dyadic adj., polyadic adj., etc. †1. Chemistry. With preceding symbol, designating an atom with a valency represented by the symbol. Cf. monadic adj. 3a, dyadic adj. b. Obsolete. rare. ΚΠ 1878 Amer. Jrnl. Math. 1 83 In any compound an arbitrarily selected group of m n-adic atoms may be replaced by a group of n m-adic atoms. 2. Mathematics. With preceding symbol or numeral (esp. the generalized symbol p, denoting a prime number), forming adjectives designating numbers expressible as a sequence of digits in the base represented by the symbol (or as a power series in this quantity). ΚΠ 1905 J. Pierpont Lect. Theory Functions Real Variables I. ii. 92 When m is used as base, the numbers a are said to be expressed in an m-adic system. 1921 Ann. Math. 23 84 The decadic integer ⋯,333,334 cannot be a 3-adic integer since the denominator of 2/3 is not prime to the base 3. 1939 Amer. Jrnl. Math. 61 894 In our case the ring of all p-adic integers o takes the place of the field of all real numbers. 1990 Proc. London Math. Soc. 60 37 (heading) Cell decomposition and local zeta functions in a tower of unramified extensions of a p-adic field. 2004 College Math. Jrnl. 35 323 Paul Monksky's elegant 1970 proof.., using Sperner's Lemma and 2-adic valuations. 3. Chiefly Mathematics and Logic. With preceding symbol (usually n), forming adjectives designating a function, operator, relation, etc., having the number of arguments represented by the given symbol. Cf. -ary suffix¹ Additions. ΚΠ 1906 Proc. Amer. Philos. Soc. 45 99 There are relations dyadic, triadic, n-adic, there are relations symmetrical, unsymmetrical transitive, intransitive. 1940 W. V. Quine Math. Logic 225 A range of n-argument functionality..is itself an n-adic relation. 1975 Notre Dame Jrnl. Formal Logic 16 87 An arbitrary k-adic operator over X(n) defined by an expression with S as the sole operator. 1992 Mind 101 137 Fusion of n singletons to form a plural class is a complex type of conjunction which conjoins n monadic universals to form an n-adic relation. 2009 V. Anashin & A. Khrennikov Appl. Algebraic Dynamics viii. 257 All compositions of basic instructions, that is, computer programs, are uniformly continuous 2-adic functions. This entry has been updated (OED Third Edition, December 2011; most recently modified version published online December 2021). < suffix1878
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