(a) Consider a sequence of closed intervals .I1=| a1, b1] . I2=[a2, b2] …Suppose that an ≤an 1 and bn 1 ≤bn for all n (Figure 8 ). Prove that there is a point x which is in every In (b) Show that this conclusion is false if we consider open intervals instead of closed intervals. The simple result of Problem 14 (a) is called the "Nested Interval Theorem." It may be used to give alternative proofs of Theorems I and 2. The appropriate reasoning, outlined in the next two problems, illustrates a gene
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(a) Consider a sequence of closed intervals .I1=| a1, b1] . I2=[a2, b2] …Suppose that an ≤an 1 and bn 1 ≤bn for all n (Figure 8 ). Prove that there is a point x which is in every In
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