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I have been a bit confused for a while on what is the best way to write a multi-variable function of an arbitrary number of input variables when writing a question or answer. My first thought is to write it as a function of a vector $f(\vec{x})$, but this somewhat conflicts with the notion that the input to a multi-variable function is a point, not a vector. This seems to be how it's taught in most multi-variable calculus classes, so writing it as a function of a vector might confuse the asker and/or lead them to incorrectly believe that points and vectors are interchangeable.

I considered explicitly saying something like "Where $\vec{x}$ is a vector from the origin to the point", but that seems too wordy. I also considered $f(x_1,x_2,...)$, but I'm not a fan of ellipsis notation (not sure if anyone else feels this way, or if it's just a quirk of mine).

So what is the best notation for it?

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    $\begingroup$ I tend to use boldface myself: $f(\mathbf x)$ (scalar-valued) or $\mathbf{f}(\mathbf x)$ (vector-valued). $\endgroup$ – J. M. is a poor mathematician May 25 '13 at 15:58
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    $\begingroup$ Just write $f(x)$. $\endgroup$ – Mariano Suárez-Álvarez May 25 '13 at 15:59
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    $\begingroup$ As with a similar question that was posted on meta a while ago, I don't see why this was not posted on the main site. $\endgroup$ – Mariano Suárez-Álvarez May 25 '13 at 16:00
  • $\begingroup$ @MarianoSuárez-Alvarez I figured this was the right place for it because it pertains to how to best write a post. $\endgroup$ – Ataraxia May 25 '13 at 16:01
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    $\begingroup$ It pertains to how to write math. That that math will be in a post is quite irrelevant :-) Do you expect that there is a different «best way» to write multi-variable functions in other mediums? $\endgroup$ – Mariano Suárez-Álvarez May 25 '13 at 16:02
  • $\begingroup$ @MarianoSuárez-Alvarez Oh ok. Good to know! $\endgroup$ – Ataraxia May 25 '13 at 16:04

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