For $\displaystyle n \in {\mathbb {N}}$, define$\displaystyle I_n$= $\displaystyle [{a_n, b_n}]$ to be a sequence of closed and bounded intervals such that $\displaystyle I_1\supseteq {I_2} \supseteq {I_3} ...$

Prove that there is a real number $\displaystyle x$ such that $\displaystyle x \in I_n$ for all $\displaystyle n$ i.e.

$\displaystyle {^\infty}$

$\displaystyle \bigcap {I_n}{\neq}{\oslash}$

$\displaystyle _{i=1}$