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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 $(((3+4)\cdot 4)^4)^{1/2}$

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    $\begingroup$ 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., $\big( \text{ and } ( \ldots ) \text{ and } \big)$ ...) $\endgroup$ – Benjamin Dickman Oct 3 '15 at 20:27
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    $\begingroup$ 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. $\endgroup$ – Karl Oct 3 '15 at 21:32
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    $\begingroup$ @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". $\endgroup$ – vonbrand Oct 3 '15 at 23:27
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    $\begingroup$ For purposes of priority, it's inner to outer. No nead for different shape brackets. $\endgroup$ – JTP - Apologise to Monica Oct 4 '15 at 1:18
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    $\begingroup$ @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. $\endgroup$ – Daniel R. Collins Oct 4 '15 at 21:13
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It is definitely not wrong to teach your students to just use (). I would possibly argue the converse. Your experience at school flys in the face of convention. Teaching your students that way will not prepare them well for meeting the rest of the world.

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I teach the students to use parentheses only. They are widely acceptable and it is what I prefer to use. One argument against brackets is that some students find it hard to remember how to draw different kinds of brackets and spend inordinate amounts of time shaping their brackets.

However I find that it is important to show students that different brackets may be used as parentheses and are not only used for matrices or the floor function. When students find an expression with different brackets they need to be able to understand it and know how to evaluate correctly.

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  • $\begingroup$ I'm used to [ ] being used in place of ( ), but I would never expect to see { } used that way. $\endgroup$ – Jessica B Oct 4 '15 at 15:16
  • $\begingroup$ @JessicaB As an upper elementary school teacher I have seen { } used that way, but not often. Students who haven't seen them before are often thrown by them. $\endgroup$ – Amy B Oct 7 '15 at 0:08
  • $\begingroup$ As research mathematician who hasn't seen them before, I would be thrown by them. $\endgroup$ – Jessica B Oct 7 '15 at 6:56

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