I have a set theory problem (something to do with cardinals, I think):

Let $\displaystyle A$ be non-empty and $\displaystyle R \subseteq A \times A $ relation in which holds $\displaystyle \forall x \exists y (yRx) $. Show that there exists funtion $\displaystyle f: \omega \rightarrow A $ so that $\displaystyle f(n+1)Rf(n) $ with every $\displaystyle n \in \omega $.

I was thinking to use induction, but how construct the set for that? Is it something like

$\displaystyle T = \{n \in \omega \mid A \approx n \Rightarrow \exists f: \omega \rightarrow A (f(n+1)Rf(n))\} $ ?