Suppose SCR (S is a proper subset of R) is bounded above and nonempty. If sup...

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Suppose SCR (S is a proper subset of R) is bounded above and nonempty. If sup S is not an element of S then use a direct argument using the "approximation of the sup" to show that S is infinite. Start with = 1, find x1 € S then look in (x1, sup S) for x2. Repeat this argument to create an infinite number of elements of S. Be sure to write all of the details. Suppose SCR (S is a proper subset of R) is bounded above and nonempty. If sup S is not an element of S then use a direct argument using the "approximation of the sup" to show that S is infinite. Start with = 1, find x1 € S then look in (x1, sup S) for x2. Repeat this argument to create an infinite number of elements of S. Be sure to write all of the details.

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