SOLUTION: Does the commutative property imply the associative property in number systems?

Question 473970: Does the commutative property imply the associative property in number systems?

Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Not necessarily, e.g. dot products are commutative but they are not associative. Also, what is the dot product of a scalar and a vector?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The two properties deal about two different things.
Commutativity talks about how rearranging the ORDER of the factors affects the product, whereas associativity talks about the effects various groupings of the factors have on the product, WITH THE ORDER OF THE FACTORS KEPT FIXED.
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