Show that $x\mapsto \frac{1}{x}$ is not uniformly continuous for $x \in (0,1), \frac{1}{x} \in \mathbb{R}$ I am meant to show that for $x \in (0,1)$,  $\frac{1}{x}$ is not uniformly continuous. 
I am able to come up with a proof but the given hint tells me to investigate $x_n = \frac{1}{n}$, $y_n = \frac{1}{n+1}$ and I'm not sure how to use that to construct a proof. 
Is it something to do with Cauchy sequences?

Or even simpler(?): A uniformly continuos function on a bounded domain is bounded.
