moduloprep.adj.
/ˈmɒdjᵿləʊ/, /ˈmɒdʒᵿləʊ/, U.S. /ˈmɑdʒəˌloʊ/ Mathematics.
A. prep.
a. With respect to a modulus of (a specified value). See modulus n. 2b. Cf. mod prep.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > with respect to a modulus [preposition]
mod1854
modulo1887
1887 Amer. Jrnl. Math. 10 62 A linear transformation is said to be ‘congruent to identity modulo k’ if all the coefficients are divisible by k except those on the principal diagonal, the latter being congruent to 1 (modulo k).
1897 Bull. Amer. Math. Soc. 3 381 Congruences irreducible modulo p (p = prime).
1903 J. Bowden Elem. Theory Integers x. 242 The statement of congruence is written α ≡ β (mod. μ), which is read ‘α is congruent with β, modulo μ’
1939 L. E. Dickson Mod. Elem. Theory Numbers i. 8 Any positive integer n is congruent modulo 9 to the sum s of its digits.
1966 C. S. Ogilvy & J. T. Anderson Excursions Number Theory iv. 43 Since 8, 15, 22, 29, etc., and also —6, —13, etc. are all congruent to 1 (mod 7), they are members of the same residue class modulo 7... In arithmetic modulo 7, 8 is equivalent to 1 in many senses.
1987 J. Millman & A. Grabel Microelectronics (ed. 2) viii. 331 A chain of n binaries will count up to the number 2n before it resets itself into its original state. Such a chain is referred to as a counter modulo 2n.
b. In extended use. (a) With respect to an equivalence defined by (some feature), disregarding differences indicated by (some unimportant feature); (b) taking into account (a particular consideration, aspect, assumption, etc.).
ΚΠ
1953 W. Ambrose Let. in S. Nasar Beautiful Mind (1998) xx. 155 [John Nash] proceeded to announce that he had solved it, module [sic] details.
1962 Jrnl. Philos. 59 776 Which we choose is entirely arbitrary, but (modulo the assumption that any run covers a line segment) it determines how we answer the question [etc.].
1973 C. C. Chang & H. J. Keisler Model Theory 7 The language is determined uniquely, modulo the connectives, by the sentence symbols.
1992 Stud. Eng. Lit.: Eng. Number (Tokyo) 161 The Navajo underlying structure is identical, modulo word order, to the one found in all the languages studied in Ch. 3.
B. adj. (attributive).
Modular; involving calculations with respect to a modulus. See modulus n. 2b.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > [adjective] > prime > modular
modular1815
modulo1966
1966 C. S. Ogilvy & J. T. Anderson Excursions Number Theory iv. 44 In number theory one must often work with very large numbers. If these can be reduced to equivalent smaller numbers, much time-consuming labor can be avoided. Herein lies one of the great contributions of modulo arithmetic.
1993 S. A. Maguire Writing Solid Code 134 These are the same programmers who would have written the division and the modulo operations using bitwise operators.
This entry has been updated (OED Third Edition, September 2002; most recently modified version published online March 2022).
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prep.adj.1887