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    proofs of least upper bounds

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    1. If supS=a and X={s-k l s element of S}. Prove that supX = a-k

    2. If A and B have least upper bounds, prove sup(AUB) = max(supA, supB)

    3. Prove for all x<supS there exists y that is an element of S such that x<y< or = supS.

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