(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

let [itex]A_{1}, A_{2}, ....[/itex] be a sequence of subsets of R such that the intersection of the [itex]A_{1}, A_{2}, A_{3}...., A_{n} [/itex] is nonempty for each n greater than/equal to 1. Does it follow that the intersection of all [itex]A_{n}[/itex]'s is nonempty?

Does the answer change if you are given the extra information that each [itex]A_{n}[/itex] is a closed interval, that is a set of the form [itex][a_{n}, b_{n}] = {x member of R : a_{n} \leg x \leq b_{n}[/itex] for some pair of real numbers [itex](a_{n},b_{n})[/itex] with [itex]a_{n} < b_{n}[/itex]

2. Relevant equations

3. The attempt at a solution

I don't really have a clue how to start this. It seems to me that in both cases it should be non empty, but I'm really not sure. I'm not looking for some one to do this for me, because I want to be able to do it myself - I would appreciate it if someone could point me in the right direction without giving the game away.

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# Homework Help: Intersection of Sets

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