# Talk:Reciprocal

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## Untitled

I can't understand the problem..

that question is 'The reciprocal of a nonzero interger is an interger..' i have to prove this problem.. if the sentense is a fault, explain why or give an example thatshows it is flase.

• I don't think this is the place, but... If ${\displaystyle a\in I}$, then the reciprocal of ${\displaystyle a}$ is ${\displaystyle {\frac {1}{a}}}$, which is never integer unless ${\displaystyle a\equiv 1}$.

## Requested move 18 April 2017

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: Not moved. There is no consensus that the primary topic is the mathematical term. — Martin (MSGJ · talk) 09:43, 4 May 2017 (UTC)

ReciprocalReciprocal (disambiguation)Multiplicative inverse is the primary topic for "reciprocal". Reciprocal in its current disambiguation form should be moved to Reciprocal (disambiguation) (which is, as one would expect, now a redirect to Reciprocal); and turned into a redirect to Multiplicative inverse. TJRC (talk) 22:42, 18 April 2017 (UTC) --Relisting. GeoffreyT2000 (talk) 00:45, 26 April 2017 (UTC)

• Comment. I would like to see some actual evidence that multiplicative inverse is the primary meaning, rather than relying on our intuition for this. I can easily believe that it is the most basic meaning, or the meaning that learned at the earliest age in school. But when I do e.g. a Google scholar search for "reciprocal", the top hits go on for pages with other meanings and the multiplicative inverse meaning is nowhere to be found. The same goes for a Google book search. —David Eppstein (talk) 23:11, 18 April 2017 (UTC)
Fair point. The Wikipedia article traffic statistics page is getting an "internal server error" right now, so I couldn't check page views. My take is that there are only three articles on this page for which "reciprocal" is a synonym; that is, only three pages where a user might reasonably expect to be taken when looking up "reciprocal". (All of the others use the term or a variant of it as a qualifier, e.g. "Reciprocal spiral", "Reciprocal determinism", etc.; no one will ever expect to land on any of those pages from "reciprocal", and I think we can safely exclude them from any possibility of being the primary topic.)
The three are Multiplicative inverse, Reciprocal (grammar) and Hybrid (biology). "Reciprocal" is used only once in Hybrid (biology), and while I might even expect it to have more page views than Multiplicative inverse, I would be very skeptical if someone suggested that those page views were due to someone coming in from the disambiguation page, having looked up "reciprocal" first. And "reciprocal" in the grammar sense is a two-paragraph stub; I don't think it's getting a lot of action. For what it's worth (and I realize it's not), the multiplicative inverse is the only common example of "reciprocal" used as a noun, as opposed to a qualifier of another concept, that I'm aware of. I realize it's dangerous to extrapolate from a sample of one, but I think that's supported by the sparse use in one article and the shortness of the other.
Hopefully, the stats page will be back up tomorrow and I can have a more analytical look at it.
In terms of incoming links, Multiplicative inverse has about 320; Reciprocal (grammar) has 43; and Hybrid (biology) has a whopping 3000+, but it's unlikely that a significant number of those come from use of "reciprocal". TJRC (talk) 00:29, 19 April 2017 (UTC)
@TJRC: stats.grok.se has not been used in at least a year and a half. Use PageViews, which is officially supported. --Izno (talk) 00:41, 19 April 2017 (UTC)
Thanks for that @Izno:. I haven't proposed an RM in longer than I thought.
A graph of the three articles I mention is at [1], and it's pretty much what I'd expect, mirroring the incoming link ratios. Hybrid (biology) has about double the hits of Multiplicative inverse; and Reciprocal (grammar) barely registers. I don't think the higher popularity of the hybrids article changes my position, though. It's extremely unlikely that those views come in from "reciprocal", while a substantial number for multiplicative inverse likely do ("reciprocal" is, after all, the common name that most people use for "multiplicative inverse"). TJRC (talk) 00:49, 19 April 2017 (UTC)
Comment: I'm not terribly surprised by the poor showing in Google scholar and Google books. In the circles represented there, the term reciprocal would be considered an informal version of multiplicative inverse, a terminology introduced in grade school perhaps, and would tend to be eschewed. On the practical side, whenever I have brought up the topic of reciprocal polynomials, I have been forced to explain that this is not referring to a multiplicative inverse–the automatic response of my students to the term "reciprocal".--Bill Cherowitzo (talk) 04:49, 19 April 2017 (UTC)

I don't think "multiplicative inverse" is the primary meaning. It's probably the meaning everyone learns first, since mathematics is required of all pupils and the term is encountered there. That's what may make it appear to some to be the primary meaning. Now notice that multiplicative inversion is an involution, i.e. if the reciprocal of a is b then the reciprocal of b is a. The relationship is reciprocated, and that, I think, is why the word "reciprocal" is used. Notice that we find the explanation of why that word is used by looking to something other than mathematics. Michael Hardy (talk) 20:39, 19 April 2017 (UTC)

• Oppose – unsupported rationale for primarytopic grab. Disambiguation is good. Dicklyon (talk) 05:17, 26 April 2017 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.