Commutative Property: The order of the objects from left to right doesn't matter.
For example : 5+3+2 = 3+2+5 = 2+3+5, etc... Because addition is commutative.
Associative Property: Where we put parentheses doesn't matter.
For example: x(yz) = (xy)z if x, y, and z are numbers.
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There is no difference - synonymous.
An axiom is a self-evident statement that is assumed to be true. A theorem is proved to be true.
an axiom is a fact/property such as "ac = ca"
"A geometry rule that we accept to be true without any proof is called an axiom." "The axiom 'might makes right' is often true in the governments of the world.
An axiom is a truth recognised universally, or an established principle or rule. It is a self-evident statement such as the famous axiom by Rene Descartes: I think therefore I am. It is obvious that were one to think, that one would be - this is self evident.