-adic, suffix
(ˈædɪk)
[f. -ad1 1 a + -ic. In sense 1 after G. -adisch (K. Hensel Zahlentheorie (1913) iii. 51); in sense 2 f. polyadic a. Cf. also monadic a., dyadic a. (n.), etc.]
1. Math. Used with a preceding symbol or numeral, esp. the generalized symbol p (denoting a prime number), to designate numbers expressible as a sequence of digits in the base represented by the symbol (or more generally as a power series in this quantity). Cf. -ary1.
| 1939 Amer. Jrnl. Math. LXI. 894 In our case the ring of all p-adic integers o takes the place of the field of all real numbers. 1974 Encycl. Brit. Macropædia XIII. 362/2 A simple illustration of the efficiency of using p-adic numbers is the statement that -1 has a square root in the 5-adic numbers. 1990 Proc. London Math. Soc. LX. 37 (heading) Cell decomposition and local zeta functions in a tower of unramified extensions of a p-adic field. |
2. Logic. Used with a preceding symbol to designate a relation having the number of arguments represented by the given symbol. Cf. *-ary1 2.
| 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 XVI. 87 An arbitrary k-adic operator over X(n) defined by an expression with S as the sole operator. 1990 Mind Cl. 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. |