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I'm writing an assignment right now and getting into some quite lengthy derivations, which caused me to wonder about bracket notation in math and what is best practice. There are three primary types of brackets I'm familiar with: the curly brackets {}, square brackets [], and the classic parentheses (). From what I learned, in an equation with tons of brackets, you go from outer to inner in that order e.g.

$$A\left\{\frac{2}{3}\left[B^2\left(C+4\right) + 2\right] - D^2\right\}$$

My question I suppose would be what happens if you need to add another level? i.e. What is the next bracket you would use? Or would needing to do that be considered bad notation and an indication that you should simplify/expand your expression?

What is accepted practice in literature? Is there a convention, and if so what is it? Do some people not even use different types of brackets? I could see a case being made that you just stick to the round brackets () for each level, just use different sizes maybe. I had trouble finding good and insightful answers so here I am on SO. I look forward to your answers.

Related but unanswered

David G. Stork
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mathwiz97
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    it's all parentheses all the time for operation grouping in programming; there, curly braces and square brackets mean very different things! - And, indeed, parentheses themselves collect additional meanings. – Dan Uznanski Jun 24 '21 at 20:29
  • related https://math.stackexchange.com/q/1875182/889261 – Quantum Mechanic Jun 24 '21 at 21:04
  • There is no agreed convention. I would avoid curly braces altogether to avoid confusion with set notation. I think lots of people just stick to round brackets and use layout and the size of the brackets to improve readability. – Rob Arthan Jun 24 '21 at 22:15
  • Given @QuantumMechanic's informative answer and reference, I will qualify my comment: I don't believe there is an agreed convention in pure mathematics. – Rob Arthan Jun 25 '21 at 00:01
  • @RobArthan I'm not even certain the convention is agreed upon in physics, I can simply attest to its existence – Quantum Mechanic Jun 25 '21 at 02:36
  • @QuantumMechanic that related thread has excellent discussion, strange it didn't come up in my search. Thank you! – mathwiz97 Jun 25 '21 at 13:53

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One convention is to repeat again in the same order. So a nested expression can look like \begin{equation} \left\{f\left[e\left(d\left\{c\left[b\left(a\right)b\right]c\right\}d\right)e\right]f\right\}. \end{equation}

Quantum Mechanic
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  • Interesting. Makes sense, but I have never seen this, though. – Giuseppe Negro Jun 24 '21 at 21:08
  • I learned this many years ago from who knows where – Quantum Mechanic Jun 24 '21 at 21:09
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    In this physics style guide they prescribe my quoted rule, so perhaps it's a physics thing https://journals.aps.org/prl/authors/bracketing-mathematical-expressions-h9 – Quantum Mechanic Jun 24 '21 at 21:16
  • @QuantumMechanic Neat -- a source like the APS is something I was actually looking for. Thanks for the insight, I had never seen that convention to repeat it. – mathwiz97 Jun 25 '21 at 13:51
  • I also found it in this ~decade-old Physical Review Style Guide (sorry I only found a pdf): https://cdn.journals.aps.org/files/styleguide-pr.pdf - there they say to put the outer set of symbols in bold! – Quantum Mechanic Jun 25 '21 at 14:37