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Abstract Algebra

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Binary Operation of Exponentiation

ABSALG-ZTTKY2

Consider $\mathbb{Z}_{>0}$ with the binary operation of exponentiation defined by $f(x,y)=x^y$.

Identify which of the following statements are true.

A

There is a left identity.

B

There is a right identity.

C

There is a two-sided identity.

D

There do not exist any left or right identities.

E

None of the above.