Frequently Asked Questions
What is the difference between associative and commutative?
Associative is about grouping (the placement of parentheses); commutative is about order. (a + b) + c = a + (b + c) is associative; a + b = b + a is commutative.
Is subtraction ever associative?
No - except trivially when c = 0. (a - b) - c = a - b - c, but a - (b - c) = a - b + c. The two match only when c = 0.
Why do some texts say (a · b) · c = a · b · c without parentheses?
Precisely because associativity holds. Math notation drops parentheses when the operation is associative; the result is well-defined without them.
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