I know that this problem is an application to the statement-
($\mathbb X$,d) is compact$\iff$Every collection of closed sets in ($\mathbb X$,d) with the finite intersection property has a non-empty intersection.
A hint given in my text-"The set $F_n=\{x,x\ge n\}$ are closed and each finite family has non-empty intersection; yet $\cap_{i=0}^\infty F_n $=$\emptyset$".
My question is what is the significance of "$n$" here.
if possible, please explain me this in detail,as i'm a beginner in topology
Thank you!