So we're given a sequence $x_n$ and a sequence $y_n$, both of them being of real numbers. We know that $x_n \rightarrow 0$ and that $y_n$ is bounded. We need to prove that $x_n y_n \rightarrow 0$.
My idea was that, since $x_n \rightarrow 0$, multiplying some number of $y_n$ by $0$ would always just be $0$, and we know that we can do this since $y_n$ is bounded (although I don't think it would matter if it were unbounded).
Am I right in thinking this, or is the answer in a completely different direction?