Should I use different parenthesis in calculations?

Question

I was taught in a school that one should denote the order of computations by different brackets like

$2\cdot \{3+[2\cdot (8+9)]\}$

Do the teachers taught me wrong as for example the notation $\{\}$ is used in sets and $[]$ in matrices and in rounding downwards? If a professional mathematician should write the formula above, should he or she write $2\cdot \{3+[2\cdot (8+9)]\}$ or $2\cdot (3+(2\cdot (8+9)))$?

Answer 1

It is not wrong either way. Use whatever parentheses that makes it easier to read. Sometimes making one set of parentheses larger helps, sometimes different bracket styles helps.

Answer 2

Different people take different approaches depending on what kind of things they are working with. If you are also writing a lot of sets with $\{\ldots\}$ notation on the same page as your formula, you might want to use only $(\ldots)$ and $[\ldots]$ to show order of computation.

On the other hand I've heard computer scientists complain about how mathematicians like to use $(\ldots)$ and $[\ldots]$ interchangeably, because computer scientists prefer to use just one symbol for one meaning (e.g., use only to mean something else and they will prefer to use only $(\ldots)$ for order of computation so they can use $[\ldots]$ and $\{\ldots\}$ for other things).

So it's all a matter of what kind of math you're doing and whom you're doing it for. In the formula you showed, the three kinds of brackets are useful because you can easily see exactly where each bracketed quantity begins and ends without having to count brackets.