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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 $2\cdot (3+(2\cdot (8+9)))$?

notsure
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    If the professional mathematician knows Latex he would simply write it as $2\cdot \Bigg(3+\bigg(2\cdot \big(8+9\big)\bigg)\Bigg)$ – najayaz Mar 10 '15 at 12:43

2 Answers2

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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.

jdods
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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.

David K
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  • "Bracket-type" symbols serve so many different purposes in mathematics that it would be tough to pin down universally accepted practices. Computer science syntax often has strict pre-defined uses, at least in an actual program in a specific language. There are simply always going to be many exceptions in "free" mathematics, i.e. more complicated constructions that require disobeying the standards. The nice thing is that mathematicians are generally good at defining their notation if it is in any way non-standard! Maybe a good analogy is typing (computer science) v.s. handwriting (mathematics). – jdods Mar 10 '15 at 14:35
  • @jdods Good point; I think the attitude of computer scientists is influenced by working with programming languages, which tend to be rigid in their interpretation of each symbol. The realm of inquiry also tends to be quite different from "pure" math although there is a large overlap. – David K Mar 10 '15 at 15:04