A sequence of closed intervals
in R {\displaystyle {}\mathbb {R} } is called (a sequence of) nested intervals, if I n + 1 ⊆ I n {\displaystyle {}I_{n+1}\subseteq I_{n}} holds for all n ∈ N {\displaystyle {}n\in \mathbb {N} } , and if the sequence of the lengths of the intervals, i.e.
converges to 0 {\displaystyle {}0} .