For each integer n>=0, let [a_n, b_n] be a closed, bounded interval in R (real numbers) such that a_n <= b_n (a_n is greater than equal to b_n). Suppose that the resulting collection of intervals is pairwise disjoint, that is if n =/ m (n is not equal to m), then the intersection of [a_n, b_n] and [a_m, b_m] is empty. Prove that these intervals do not cover all of R (real numbers).
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