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The multiplication sign $\times$ is used in many places in mathematics other than arithmetic (in set theory – denoting the Cartesian product of two sets, to name an example).

The division sign $\div$, on the other hand, is seemingly only used in arithmetic. Wikipedia's list of mathematical symbols lists the sign together with $/\!$, but only provides only one example for $\div$, i.e. its use in arithmetic.

Where else in mathematics is the division sign $\div$ (the obelus) used? Googling is of no help.

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    $\begingroup$ The question about the geometric mean was quite interesting. Why you have deleted it ? $\endgroup$ – callculus Nov 12 '16 at 17:27
  • $\begingroup$ @callculus, the things I do for you. $\endgroup$ – user376034 Nov 12 '16 at 17:38
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    $\begingroup$ Nice. I upvoted the question. $\endgroup$ – callculus Nov 12 '16 at 17:44
  • $\begingroup$ @callculus perhaps if you had upvoted it from the start, I wouldn't have deleted it. To anyone interested in what the question was (now is): math.stackexchange.com/questions/2010656/…. $\endgroup$ – user376034 Nov 12 '16 at 17:48
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It's used nowhere else that I know of. Generally, we would use / (or a horizontal fraction bar, if appropriate) for any quotient operation. The reason is likely because / is easier to produce, both handwritten (it's shorter to write) and on a computer (it's on a key most keyboards, unlike the obelus).

Another interesting point is that there are many kinds of products (cartesian product, dot product, cross product, tensor product, ...) so many symbols have been invented for them, but there are relatively few types of quotients (the ones I can think of broadly fall into two classes -- either literally the inverse of a corresponding multiplication operation, or else some kind of quotient space obtained by modding out by an equivalence relation), so one symbol is enough.

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  • $\begingroup$ In case you were wondering, it's called an obelus. $\endgroup$ – steven gregory Oct 30 '16 at 8:12

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