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I was wondering how should I rephrase the below sentence such that it is grammatically correct (accepted in standard American English):

10 modulo 3 equals 1.

Initially, I'd thought that it is grammatically correct, but dictionary.com claims that it is an adverb and not a verb, so it looks like that above usage is wrong.

What's the grammatically correct usage of the word "modulo" ?

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The classical usage would be $10$ equals $3$ modulo $1$, –  GEdgar Jan 28 '12 at 14:28
I don’t understand the question. Modulo can be preposition or an adjective. It is neither a verb nor an adverb. –  tchrist Jan 28 '12 at 15:19
@tchrist the source I provided in the question (dictionary.com) states that it is an adverb.. –  Pacerier Jan 28 '12 at 17:36
AHED, Webster, Oxford, and Wordnik all list modulo as a preposition. Dictionary.com is in a distinct minority, and I wouldn't worry about phrasing something grammatically based on its possibly erroneous categorization. –  Gnawme Jan 29 '12 at 5:53
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2 Answers

up vote 6 down vote accepted

Mathematics would say: "10 is congruent to 1 modulo 3". The modified usage "10 modulo 3" with "modulo" as an operation (like "10 plus 3") is from computer programming.

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No, modulo as a preposition is older than computer programming is. Check the OED for mod, modulo. These are from the 19ᵗʰ century (barely): the first documented use appears to be Gauss in 1801. –  tchrist Jan 28 '12 at 15:10
Yes, what I wrote is correct. It does not contradict "modulo as a preposition". –  GEdgar Jan 28 '12 at 19:29
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The verb in your sentence is equals. The entire sentence can be parsed either as 10 modulo 3 being a noun phrase with modulo 3 operating as an adjective, or as modulo 3 equals being a verb phrase with modulo 3 operating as an adverb. Whichever analysis is preferred, the usage is perfectly standard, if slightly imprecise. The reference you cite is correct to prefer is congruent to over equals.

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10 is a noun right? so 10 modulo 3 = [noun][adverb][noun] and that's a grammatical phrase? –  Pacerier Jan 28 '12 at 10:49
@Pacerier Binary operators like 4+5 or 10%3 are grammatically prepositions. Four plus five, ten modulo three. –  tchrist Jan 28 '12 at 13:18
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