A notational conventions question: It's common to write $\sin(x)$ as $\sin x$, omitting the brackets. It's not just laziness: it makes the text less busy. $\log \log n$ is easier to parse than $\log(\log(n))$. Which functions is it OK to do this for? Is $\operatorname{f} x$ OK?

@christianp I've seen omitted brackets for domain and range sometimes, like $\operator name{dom} f$ and $\operator name{ran} f$. Guess it depends on how frequently the functions are used across the branches of mathematics?

@christianp whoopsie that's supposed to be $\operatorname{dom} f$ and $\operatorname{ran} f$ (silly phone keyboard inserting spaces) but you know what I meant

@christianp I'm not a huge fan of it, but it's fairly common practice for a lot of the dynamicists I've seen give talks. Like you said, it makes the notation less busy (especially nice for writing on a chalkboard), and in that context, we're mostly concerned with composition of functions - multiplication tends to show up in predictable ways, so people aren't so worried about distinguishing the two.

@christianp I guess it's not okay to write sin x sin y, because that's ambiguous. If there's no ambiguity, and people will get it, then it's probably fine.
The notation for (sine x) squared is a little 2 in the sky after sin, and yet in other notation that would mean applying the sine function twice.

@christianp it’s extremely common for functional programmers

@christianp also, if we think about group actions then we often write g.x or g x (not g(x)) for a group element acting on x \in X, so the operator g : X —> X is denoted this way

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