# How to teach brackets?

I was taught in a school that one has to use different brackets in expressions like $\{[(3+4)\cdot 4]^4\}^{1/2}$ to denote the order which subexpression is evaluated first. But can this be recommended in current mathematics? I guess no as one can create arbitrary complex expressions such that one would require arbitrary many different bracket notations. Also, I think that is good to teach that $()$ is for evaluating order, $[]$ is for floor function and matrices and $\{\}$ is for the set notation. So is it wrong if I suggest students to use the notation $(((3+4)\cdot 4)^4)^{1/2}$

• One reason that people use parentheses (generally like this, though [on occasion] with further symbols) is to help the reader match each opening parenthesis, (, with its corresponding closing parenthesis, ). But, in fact, the proper use of parentheses should not allow for ambiguity; so the final notation that you suggest is the norm. (Nevertheless, there is an option to use larger parentheses in TeX; precede the symbol with \big and compare, e.g., $\big( \text{ and } ( \ldots ) \text{ and } \big)$ ...) – Benjamin Dickman Oct 3 '15 at 20:27
• I personally agree and would only use $()$ as the different brackets distract me. There is a lot to say for 'form of argument' . Id always go for a square root over a power half whenever possible for example. – Karl Oct 3 '15 at 21:32
• @BenjaminDickman, LaTeX prefered usage is \left( closed by \right). They can be used with all sorts of "parentesis", even non-matching ones, and the sizes get automatically adjusted to what is "inside". – vonbrand Oct 3 '15 at 23:27
• For purposes of priority, it's inner to outer. No nead for different shape brackets. – JTP - Apologise to Monica Oct 4 '15 at 1:18
• @beginnertutor: The way you were apparently taught is very nonstandard. Among other the issues others point out, consider that when shifting to computer programming one will have nothing but regular parentheses, so it's best to practice with the nested parentheses as soon as possible. – Daniel R. Collins Oct 4 '15 at 21:13