Hi guys!

Ok, last problem today! I've already read any other posts on the sandwich principle, but I've never seen it before today, and my chapter doesn't explain it, just gives a question on it! If anyone could show me how this is done I would really appreciate it!

Let $\displaystyle (a_{n}),(x_{n})$ and $\displaystyle (b_{n})$ be sequences with limits $\displaystyle \alpha,\xi,\beta$ respectively, and suppose that, for all $\displaystyle n\geq{1}$,

$\displaystyle a_{n}\leq{x_{n}}\leq{b_{n}}$

Show that $\displaystyle \alpha\leq\xi\leq\beta$ [This is sometimes called the sandwich principle. It can be useful if $\displaystyle (a_{n})$ and $\displaystyle (b_{n})$ are "known" sequences and $\displaystyle (x_{n})$ is unknown. It is especially useful when $\displaystyle \alpha=\beta$, for in this case we conclude that $\displaystyle \xi=\alpha=\beta$.]

Nice explaination, if I did actually know what $\displaystyle (a_{n})$ and $\displaystyle (b_{n})$ were!In this case I don't know what to do, can anyone help please?