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As far as I understand from this Wikipedia page, $\frac 73$ is a reciprocal of $\frac 37$;

But can a term "reciprocal" be applied to a non-fraction number?

For example, it would be correct to say:

reciprocal of $\frac 21$ is $\frac 12$

But would it also be correct to say:

reciprocal of 2 is $\frac 12$

?

brilliant
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  • Absolutely not. –  Nov 28 '20 at 03:06
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    @SenZen Can you, please, cite some sources because supporter jjagmath gave me the opposite answer below and now I am confused. – brilliant Nov 28 '20 at 03:11
  • @brilliant literally like two paragraphs beyond what you cite, they say nonzero integers are expressed as fractions over 1 and have reciprocals . – rschwieb Nov 28 '20 at 04:04
  • @rschwieb - You are citing the same source (my source) below two opposite answers. One is this one, and the other one is that of the supporter named jjagmath (below). So, which one of the two answers do you consider as correct? – brilliant Nov 28 '20 at 04:23
  • @rschwieb - "beyond what you cite, they say nonzero integers are expressed as fractions over 1 and have reciprocals" - That's exactly when they are expressed as fractions. But what about the cases when they are not expressed as fractions? That's, in fact, what my question was about. – brilliant Nov 28 '20 at 04:27
  • @brilliant my comment is not related to SenZen’s in any way other than being next to it. I do not agree with senzens comment. I agree with jjagmath’s answer. And even if neither of those things were here now, the article you cited has a complete explanation right next to what you cited. It does not say that there are “cases where integers are written as fractions” it says you can always write them as fractions. I think you are talking about a distinction that doesn’t exist. – rschwieb Nov 28 '20 at 04:29
  • @rschwieb - I see. Don't be so rude next time. – brilliant Nov 28 '20 at 04:30
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    @brilliant Sorry, I realize it is unpleasant to be called out on something like this. I could have been gentler. Good luck with your studies. – rschwieb Nov 28 '20 at 04:34
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    How are you defining reciprocal? That’s where you should start. – gen-ℤ ready to perish Nov 28 '20 at 05:07
  • @brilliant You rely on authority too much –  Nov 28 '20 at 15:55

2 Answers2

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Yes, every number have a reciprocal, except $0$. It's also called its multiplicative inverse.

jjagmath
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  • Can you, please, cite some sources because @SenZen gave me the opposite answer and now I am confused. – brilliant Nov 28 '20 at 03:10
  • @brilliant source: the wiki article you cited but didn’t read completely. – rschwieb Nov 28 '20 at 04:08
  • @rschwieb - You are citing the same source (my source) below two opposite answers. One is this one, and the other one is that of the supporter named SenZen (above). So, which one of the two answers do you consider as correct? – brilliant Nov 28 '20 at 04:23
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Yes. For instance, $\dfrac1{\pi}$ is the reciprocal of $\pi$. $\dfrac1r$ is the reciprocal of $r$ for any nonzero $r\in \Bbb R$.