1. ## functions

when a question states that A is isomorphic to B, do we define the function from A to B or from B to A?

im quite confused about how we should define the function..

thanks

2. By "the function", I suppose you mean "the isomorphism"?

Usually, when we say $\displaystyle A \cong B$, we mean that there exists an isomorphism $\displaystyle f: A \rightarrow B$. (There could be more than one.) But it doesn't really matter which direction we suppose the arrow to be going, because $\displaystyle f^{-1}$ is an isomorphism $\displaystyle B \rightarrow A$. (Prove it!)