Hi.

I'm a mechanical engineering student in a real analysis class (yeah, I'm a little cocky).

As you can imagine I'm having difficulties, but there's this one thing that I'm stopped cold on. I need to prove that:

$\displaystyle \bigcup_{n = 1}^{\infty} \left(\bigcap_{k=n}^{\infty} A_k\right) \subset \bigcap_{n = 1}^{\infty} \left(\bigcup_{k=n}^{\infty} A_k\right) $

I get the intuitive meaning of this (I think so anyway) but I can't find a way to prove it. Especially the one way mentality (ie, it's not generally a proper subset). I've tried distributive laws, writing it out as English, and of course making up BS hoping to get a result that I can refine later. Waste of my precious Saturday so far.

To answer your question: yes, I registered just to ask. Sorry. Thanks in advance!