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Expert: - 5/2/2007


Question
Can you give me any examples of mathematical entities that do not obey the associative law?

(A*B)*C  is not the same as  A*(B*C)
(A+B)+C  is not the same as  A+(B+C)

Thank you for your opinions.
Jeff  

Answer
Hi, Jeff,

Sorry, but no obvious examples come to mind that involve addition or multiplication.  Obviously, subtraction and division are examples of operations that are non-associative, but for general systems that are non-associative you have to look into very advanced stuff, like Lie groups and such. [which I don't know anything about]

Possibly there are some symmetry groups that are non-associative under the operation of composition, but I am not sure.  

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