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The following is alpha of t times x:

$\alpha(t)x$

The following is alpha times t times x:

$\alpha(t)x$

My instructor had one interpretation, I used the other. ;)

Is there an easy or standard way to signify that we're talking about a function rather than a variable multiplication here?

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    @Raphael: It was a scenario where I couldn't ask them.2011-11-19

3 Answers 3

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Just a suggestion: we can simply write $\alpha t x$ to mean the product of the three variables. Usually it is clear from the context what the meaning is: if $\alpha$ is a function, then $\alpha (t)$ would be the function evaluated at $t$.

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    @Raphael: It wasn't defined.2011-11-19
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For "alpha times t times x" I would suggest writing $ \alpha\cdot t\cdot x $ and adding brackets if appropriate, like $(\alpha\cdot t)\cdot x$. You could also leave the centered dots.

The bracket in $\alpha(t) x$ does not make much sense.

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I have noticed that misinterpretations of notation are becoming more common. For instance, many students have difficulty when differentiating something such as y = sin(tan(x)), mistakenly interpreting it as a product as opposed to a composition. Jasper makes a good point when he emphasizes that the context is usually a good guide as to how to interpret. In my example, the function sine has to act on something, which would be tan(x). As a rule, if you are unsure how to interpret, ask for clarification. If the situation does not allow that, or the instructor declines to comment, closely examine the context.

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    It is only less ambiguous than your example if you accept $\sin$ to be a function. Maybe $s, i, n$ are natural numbers? Or $\sin$ is one?2011-11-18