non-associative mathematics?

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.

Answer 1

These properties are always going to work for real numbers, but yes, there are other concepts in mathematics where these won't hold. Though they require a new definition of what exactly we mean by "multiplication" and "addition". For example, if we take * to mean the cross product, the associative rule doesn't necessary hold for vectors. If we take it to mean the dot product, then it doesn't hold either.

And by the way, these aren't my "opinions"!