Say I have the following
$\bigcap_{n \in \mathbb{N}} \left(-\frac{1}{n}, \frac{1}{n}\right)$
What is the value of this intersection of an infinite amount of open sets?
Say I have the following
$\bigcap_{n \in \mathbb{N}} \left(-\frac{1}{n}, \frac{1}{n}\right)$
What is the value of this intersection of an infinite amount of open sets?
HINT: There is exactly one real number in that intersection: what is it? Once you’ve identified it, you should go on to prove that if $x$ is any other real number, then there is some $n\in\Bbb Z^+$ such that $x\notin\left(-\frac1n,\frac1n\right)$.