Associativity

In mathematics, associativity is a property that a binary operation can have. It means that, within an expression containing two or more occurrences in a row of the same associative operator, the order that the operations are performed does not matter as long as the sequence of the operands is not changed. That is, rearranging the parentheses in such an expression will not change its value. Consider for instance the equation Even though the paren... more

In mathematics, associativity is a property that a binary operation can have. It means that, within an expression containing two or more occurrences in a row of the same associative operator, the order that the operations are performed does not matter as long as the sequence of the operands is not changed. That is, rearranging the parentheses in such an expression will not change its value. Consider for instance the equation Even though the parentheses were rearranged (the left side requires adding 5 and 2 first, then adding 1 to the result, whereas the right side requires adding 2 and 1 first, then 5), the value of the expression was not altered. Since this holds true when performing addition on any real numbers, we say that "addition of real numbers is an associative operation." Associativity is not to be confused with commutativity. Commutativity justifies changing the order or sequence of the operands within an expression while associativity does not. For example, is an example of... less