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Clarifying the meaning of reciprocal

  1. Jul 2, 2011 #1
    I'm trying to get something straight. The multiplicative inverse or reciprocal is y=1/x, suggesting you just flip one to get the other. Can that numeral 1 sometimes be any number (in which case you're no longer flipping it) and still be a reciprocal? Using the relationship between heart rate (bpm) and cycle length (in milliseconds), for example, HR = 60,000/CL. In this case the equation would read y=c/x instead. How does that change anything?
     
  2. jcsd
  3. Jul 2, 2011 #2
    Hi Kriegh! :smile:

    I'm not sure what you mean... Did you ask if c/x could ever be the reciprocal of 1? The answer is no. Only for c=1 do you get the reciprocal...
     
  4. Jul 2, 2011 #3
    saying that c is not equal to x- then definitely no.
     
  5. Jul 2, 2011 #4

    Stephen Tashi

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    Perhaps the question involves the difference in meaning between "reciprocal of a number" and "reciprocal relationship". This is the difference between "multiplicative inverse" and "inversely proportional".
     
  6. Jul 2, 2011 #5

    HallsofIvy

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    Good point! The "reciprocal" of a number, c, is 1/c. But two quantities, x and y, are "reciprocally proportional" or, more commonly, "inversely proportional", if and only if x= k/y for some number k (and, of course, it follows that y= k/x).
     
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