# Bracket notation convention and accepted use

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.

• 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. Jun 24, 2021 at 20:29
• Jun 24, 2021 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. Jun 24, 2021 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. Jun 25, 2021 at 0:01
• @RobArthan I'm not even certain the convention is agreed upon in physics, I can simply attest to its existence Jun 25, 2021 at 2:36

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