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I never encountered the $\times$ symbol denoting multiplication (of real numbers or real-valued functions) since middle school until I found it recently in the measure theory notes by D H Fremlin. Since it seems to me that this author writes in a quite consistent and well-considered style, I just wondered if there is any philosophy behind the use of this symbol and, more important, if other working mathematicians would immedeatly get what is meant by it or if they would, like me, be a little bit puzzled at first.

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  • $\begingroup$ I think it's that if you want to make it explicit then don't just put the two things together (eg ab = c) and don't use a period, use 'x'. eg 4x5 = 20 $\endgroup$ – user117644 Mar 8 '15 at 12:09
  • $\begingroup$ Makes sense, thanks. $\endgroup$ – fweth Mar 8 '15 at 12:10
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    $\begingroup$ I learned to write four times five as $4\cdot 5$ in school (this differs from country to country). In higher mathematics, $\times$ is usually reserved for more "abstract" multiplication, like if you have a $2\times 2$ matrix $\left(\matrix{1&2\\3&4}\right)$, or for what is called product of spaces, such as $\Bbb R\times \Bbb R$ to signify the common Euclidian $xy$-plane. $\endgroup$ – Arthur Mar 8 '15 at 12:16
  • $\begingroup$ Mathematica will insert "$\times$" into certain expressions, transforming, for instance, "3 2 Sin[x]" into "3$\times$ 2 Sin[x]". WolframAlpha does the same. It's also worth noting that the LaTeX command for "$\times$" is "\times". $\endgroup$ – Blue Mar 8 '15 at 12:16
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    $\begingroup$ The number of different kinds of products there may be greatly exceeds the number of common symbols we have for representing them. If an author used $\times$ for inner product I'd be disconcerted, but for the usual multiplicative field operation over $\mathbb R$ it seems fine. $\endgroup$ – David K Mar 8 '15 at 12:24
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I find that $\times$ is not used often. The problem is that it looks like $x$, especially in print. I see it used most often when only working with numbers. Something like $4\times9+4$, or when $\times$ means something specific like the cross product. It may also be used for Cartesian product.

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