In mathematics and related subjects, understanding a mathematical expression depends on an understanding of symbols of grouping, such as parentheses (), square brackets [], and braces {}[1] (see note on terminology below).
Beyond elementary mathematics, [] are mostly used for other purposes, e.g. to denote a closed interval, or an equivalence class, so they appear rarely for grouping.
In the United States, the term denotes [], known elsewhere as "square brackets".
In the United Kingdom and many other English-speaking countries, "brackets" means (), known in the US as "parentheses" (singular "parenthesis").
That said, the specific terms "parentheses" and "square brackets" are generally understood everywhere and may be used to avoid ambiguity.
If two of these symbols are used, one on the left and the mirror image of it on the right, it almost always indicates a set, as in
The bar is also a symbol of grouping in repeated decimal digits.
In most mathematics, the operations of addition and multiplication are associative.
This means that once the associative law is stated, the parentheses are unnecessary and are usually omitted.
If we were to express this idea using symbols of grouping, the factors in a product.
In understanding expressions without symbols of grouping, it is useful to think of subtraction as addition of the opposite, and to think of division as multiplication by the reciprocal.