Sorry if this is in the wrong section, please move it if it is.

So I'm not very good with this real analysis stuff, this whole new definition of a convergent sequence has thrown me off.Suppose that ${y_n}$ is a sequence of real numbers. Then $y_n \rightarrow \infty $ as $n \rightarrow \infty $ means that for every $M \in \mathbb{R}$, there exists $N \in \mathbb{N} $ such that

$n \geq N \Rightarrow y_n > M$

Suppose that $x_n > 0$ for all $n$ and $x_n \rightarrow 0$ as $n \rightarrow \infty$. Prove that $\dfrac{1}{x_n} \rightarrow \infty$ as $n \rightarrow \infty$

Since $x_n \rightarrow 0$ as $ n \rightarrow \infty$ there exists $N \in \mathbb{N}$ for every $M \in \mathbb{R}$ such that $ n \geq N \Rightarrow x_n < M$

I've pretty much just copied the first line of the question, but I don't know where to start... can anyone point me in the right direction?