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A binary operation is said to have the associative property or to be associative if for all . Associativity is one of the most basic properties an operation can have.
For instance, the operation "" on the real numbers is associative because for all real numbers .
If we have an operation which is written between its arguments (like "" or "" conventionally are), associativity tells us that we may write unambiguously -- it does not matter which pair we combine first.
For a non-example, consider the operation given by . This operation is not associative because while and those expressions are not equal for all choices of (in particular, they differ whenever ).