- #1

pyfgcr

- 22

- 0

**The Nested interval theorem:**If A

_{n}= [a

_{n}, b

_{n}] is a sequence of closed intervals such that A

_{n+1}[itex]\subseteq[/itex] A

_{n}for all n [itex]\in[/itex] N, then [itex]_{n \in n}\bigcap[/itex]A = ∅.

I think of the case where a1=a2=...=an and b1=b2=...=bn for all n, hence every set A(n+1) will be the "subset" of A(n) and the intersection is the original closed interval. So I think the theorem in my textbook have some problem. Any correction for this ?