If an operation for positive integers, denoted by the temporary symbol *, is defined by
$$\alpha*\beta=\alpha^{\beta}$$
Is it commutative? Is it associative?
Please, explain me.

Question

If an operation for positive integers, denoted by the temporary symbol *, is defined by 
$$\alpha*\beta=\alpha^{\beta}$$
Is it commutative? Is it associative?
Please, explain me.

inkyvoyd · Answer

well 3^5=/=5^3 so it is not commutative.

inkyvoyd · Answer

(2^3)^4=/=2^(3^4) so it is not associative either.

inkyvoyd · Answer

since those are positive numbers, and commutativity/associativity hold only if all exampels from the entire domain hold, I have just proved that they are not commutative nor associative.

anonymous · Answer

He proved it by giving you what are called "counterexamples"

inkyvoyd · Answer

@BangkokGarrett , @Loser66 probably understands, I am just mocking him because he's helped me solve my questions on post-calculus topics before :)

loser66 · Answer

@inkyvoyd thanks for the help. One more thing: if you want to say something to me, don't mock  because I will not understand!! hihihi... I am not good at English.