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The Four Kinds of Bracketing in Mathematica

There are four kinds of bracketing used in Mathematica. Each kind of bracketing has a very different meaning. It is important that you remember all of them.
(term)parentheses for grouping
f[x]square brackets for functions
{a,b,c}curly braces for lists
v[[i]]double brackets for indexing (Part[v, i])

The four kinds of bracketing in Mathematica.

When the expressions you type in are complicated, it is often a good idea to put extra space inside each set of brackets. This makes it somewhat easier for you to see matching pairs of brackets. v[[ {a, b} ]] is, for example, easier to recognize than v[[{a, b}]].