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Let's say I have an X number and I want to increment it by 50%, I would get

$X*A=Y$

Then in order to multiply Y and get X again I would need to do

$Y*Z=X$

How do you call the relation between A and Z?

Example with numbers:

$$5*1.5=7.5$$ $$7.5*Z=5$$ $$Z=0.66$$

How do you call the relation between 1.5 and 0.66 when $X*1.5*0.66=X$?

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A and Z are multiplicative inverses; i.e., A × Z = 1.

Therefore, X × A × Z = X

Usually, we just say that A is the inverse of Z (and vice-versa).

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    $\begingroup$ I prefer 'reciprocal' to just 'inverse', but 'multiplicative inverse' is the most specific and least ambiguous. $\endgroup$ – starrise Feb 26 '16 at 0:55
  • $\begingroup$ Thanks! What's the difference between both definitions? $\endgroup$ – Fraaaan Feb 26 '16 at 1:06
  • $\begingroup$ In my experience (BS in math from a US institution) 'reciprocal' and 'multiplicative inverse' are more-or-less equivalent. The term 'inverse' by itself, without the word 'multiplicative' attached, carries a lot of mathematical baggage in that it is used for many different things. Function inverses, inverses of binary operators (addition, multiplication, Fourier transform, etc), inverse mappings, etc. Hence why I prefer 'reciprocal' or 'multiplicative inverse' as they are unambiguous and don't require context to understand. $\endgroup$ – starrise Feb 26 '16 at 1:31
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    $\begingroup$ @Fraaaan: There are many kinds of inverses: matrix inverse, trigonometric inverse (for example arcsine is the trigonometric inverse of sine but is not defined as 1/sine) etc. But generally reciprocal refers to multiplicative inverse. However, note that in some fields like engineering and physics there could also be many different concepts that have the name reciprocal $\endgroup$ – slebetman Feb 26 '16 at 4:39

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