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Prove: Let x and y be bounded sequences such that xn ≤ yn for all n...

Prove: Let x and y be bounded sequences such that xn ≤ yn for all n ∈ N. Then lim supn→∞ xn ≤ lim supn→∞ yn and lim infn→∞ xn ≤ lim infn→∞ yn.

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