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## Homework Statement

Prove that any two cyclic groups of the same finite order are isomorphic

## Homework Equations

## The Attempt at a Solution

So I began by looking at the map ##\phi : \langle x \rangle \to \langle y \rangle##, where ##\phi (x^k) = y^k##. So, I went through and showed that this is indeed an isomorphism. But when I looked at the proof in the book, is said that you first must show that this map ##\phi## is well-defined. My question here is when do I know when I should show explicitly whether a map is well-defined or not? To me it seemed relatively obvious, so I wouldn't have thought to...

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