Given two distinct infinite cardinals, $\mu<\pi$, Wikipedia states that $\kappa=\pi$ is the only possible solution of the equation $\mu\cdot\kappa=\pi$, so that one could say that $\pi/\mu=\pi$. It also states that this relies on the axiom of choice.
My question is, how can one see this?
If I have $\lvert X\rvert=\pi$ and $\lvert Y\rvert=\mu$, how can I describe and prove the existence of an injection from $X\times Y$ to $X$, using the axiom of choice?
(This question arose out of some considerations related to this post).