Suppose $\displaystyle U$ and $\displaystyle V$ are pointsets of $\displaystyle \mathbb{R}$. If $\displaystyle U$ and $\displaystyle V$ both have a leftmost point, prove that the union $\displaystyle U \cup V$ also has a leftmost point.

I can kind of see how this would be true, but I am having a lot of trouble formalizing a proof. If someone could help me along that would be great. I have just started this course, and it's a little difficult to get used to.