Question: Theorem 1.20 (Nested interval theorem). If (In)nN is a nested sequence of nonempty closed bounded intervals, then the set E := nN In =

Theorem 1.20 (Nested interval theorem). If (In)nN is a nested sequence of nonempty closed bounded intervals, then the set E := \ nN In = x R : x In for all n N is nonempty (that is, it contains at least one element). Moreover if (In) 0, 3 where (In) denotes the length of interval n, then E contains exactly one element Show that E = [sup A, inf B]

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