Question: Let (an) be an increasing sequence, (bn) be a decreasing sequence, and assume that an < bn for all n N. Show that lim(an)

Let (an) be an increasing sequence, (bn) be a decreasing sequence, and assume that an < bn for all n ∈ N. Show that lim(an) < lim(bn), and thereby deduce the Nested Intervals Property 2.5.2 from the Monotone Convergence Theorem 3.3.2.

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