Could someone please help me with this question

Please state all definitions and theorems that you will need: Corollary 3.5.8 (Nested Intervals Theorem) Let F = { An: n E N} be a family of closed bounded intervals in R such that An +1 C An for 00 all n E N . Then n An * 0. n =1 Theorem 3.5.5 (Heine Borel) A subset S of R is compact iff S is closed and bounded. Show that compactness is necessary in Corollary 3.5.8. That is, find a family of intervals { An : n E N} with An+1 C An for all n, An = 0, and such that The Sets are all bounded. n=1