Use the Monotone Convergence Theorem (MCT) to prove the Nested Interval Property (NIP) (i.e. you need to prove that given a family of nested closed intervals {In = [an, bn]} there is an x ER satisfying an ≤x≤ bn for all n € N). [Hint: Use the fact that the sequence {an} is increasing and bounded above, by b₁ for instance, and then apply MCT.]

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