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Let's say you're given an operation table for a certain operation. If you want to know if it's commutative you just look at the diagonal and see if the table is symmetric around it. Now is there something similar but this time for an associative operation? If not, is there some visualization (like an operation table) by which we can easily see if some operation is associative?

aaaaaaaah
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Simple proposition, following your ideas with operation tables:

If you write $Op(., .)$ your operation, have a table of $Op(a, Op(b, c))$ and one of $Op(Op(a, b), c)$. If both tables are identical, then you can make the assumption that the operation is associative!

Milloupe
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