Rfd-redundant: Looks like the attributive use of a noun, also redundant to the definition given in the adjective section. It was previously removed by an IP who was probably right, but I brought it here anyway. —Internoob (Disc•Cont) 03:54, 21 August 2010 (UTC)
I think we tend to RFV these and look for citations showing that it's an adjective. I don't object to deleting it, however. Mglovesfun (talk) 13:43, 21 August 2010 (UTC)
Keep. There are two different pronunciations for the word when preceding a noun that correspond to distinct sets of meanings, possibly with some overlap. "An arithmetic class" is a class in arithmetic, with pronunciation as the noun, stressing the antepenult. "An arithmetic progression" is the most common collocation, I think, of the adjective, stressing the penult. There are some cases where it is not obvious to me which pronunciation would be natural. I think we could possibly do a better job in differentiating the definitions or attributive use of the noun (pronunciation 1) and true adjective use (pronunciation 2), but the "mathematics" context tag for the overlapping sense seems to be a reasonable approximation to the usage.
In "general" usage "arithmetic progression" may be the only collocation with that pronunciation. That seems to be the view of Merriam-Webster who don't show "arithmetic" as a true adjective, but have a separate entry for arithmetic progression. I think it can be shown that arithmetic is a true adjective in other uses, meeting the modification-by-too-or-very test (and carefully excluding adjective use of "very"). DCDuringTALK 15:02, 21 August 2010 (UTC)
Arithmetic (stress on met) is used as an adjective in — off the top of my head — "~ progression", "~ series", ~ number theory/-rist/-retician ", "~ algebraic number theory/-rist/-retician ", and "~ variety". (I suspect cites can be found with very, more, or less.) But that's the adjective. The noun "(modifying another noun) Of, involving or relating to arithmetic", the one nominated, is fully redundant to the first noun sense, "The mathematics of numbers...": delete.—msh210℠ (talk) 16:57, 23 August 2010 (UTC)
Delete. This sense is not even pretending to be a separate sense; the noun arithmetic, like most nouns, can be used attributively, and this sense is documenting that fact. If it were in an ===Adjective=== section, then we could argue over whether it is in fact a distinct adjective, and request cites that demonstrate the fact; but it's not, so we can't. (But, as DCDuring says, it's not fair to describe this sense as "redundant to the definition given in the adjective section", given that it's pronounced differently.) —RuakhTALK 17:16, 23 August 2010 (UTC)
We now have only a mathematics sense for one of the not-too-numerous words with mathematical content that have normal-person meanings. Can we also have an ordinary sense? I thought context tags are supposed to indicate usage context, not subject/topic. I don't think that normal people use the penult pronunciation for anything other than arithmetic progression, nor that they use arithmetic as a true adjective.
I suppose that we can assume that no language learner will ever be more confused by the pronunciation difference than by our efforts to explain it. DCDuringTALK 17:43, 23 August 2010 (UTC)
I'm not sure which sense you're referring to as the "mathematics sense for [a word] with mathematical content that ha[s a] normal-person meaning". If you mean the first noun sense, "The mathematics of numbers...", I think that that is the normal-person meaning, and that the math context should simply be removed.
I don't think "normal" people use arithmetic progression either, but may well be wrong. The two adjective senses we have now seem quite correct and distinct from one another. The first, "Of, relating to, or using arithmetic", is pronounced differently from the noun, so probably deserves a separate sense line even if it doesn't meet the usual criteria of being an adjective. (Perhaps that should be a one of them.) It may, though, as I noted above.—msh210℠ (talk) 17:05, 24 August 2010 (UTC)
Err on the side of keep. While "arithmetic" in the sense of "Of, relating to, or using arithmetic" could be a mere attributive use of the noun, the same-sense-synonym "arithmetical" not so. As an auxiliary check, some OneLook dictionaries do have this adjective sense. I do not think that "arithmetical" in "arithmetical hierarchy" is an adjective while "arithmetic" in "arithmetic hierarchy" is a noun used attributively. --Dan Polansky 13:45, 14 November 2010 (UTC)
Seems to be already deleted (?)... oh well. striking, then. -- Prince Kassad 10:00, 18 March 2011 (UTC)
In Wikipedia, we read the beginning of the current article "Elementary_arithmetic": “Elementary arithmetic is the simplified portion of arithmetic which is considered necessary and appropriate during primary education. It includes the operations of addition, subtraction, multiplication, and division. It is taught in elementary school.” And the current introduction of "Division_(mathematics)" finishes with these sentences. “Teaching division usually leads to the concept of fractions being introduced to students. Unlike addition, subtraction, and multiplication, the set of all integers is not closed under division. Dividing two integers may result in a remainder. To complete the division of the remainder, the number system is extended to include fractions or rational numbers as they are more generally called.” So, in common arithmetic,all the numbers are rational. For example, the number √2 is irrational, and √2 is not an arithmetical writing. The current definition of “arithmetic” is wrong, because a given real or complex number is not always rational.
— Ceciliia 08:24, 3 October 2011 (UTC)