Most binary operations in which we are interested distinguish themselves from arbitrary ones in that they have the following property.
Definition
a * (b * c) = (a * b) * c
A binary operation * : V × V -> V is
called associative if, for all a, b, c
V,
For an associative binary operation brackets are superfluous:
Theorem
If a binary operation is associative, then each positioning of brackets leads to the same result.
This theorem indeed implies that it is not necessary to use brackets for
associative binary operations. Therefore we will often omit the brackets.