Upper Bounds and Supremums

Suppose that A is contained in the set of all real numbers and is bounded above. Prove that if A contains one of its upper bounds, then this upper bound is sup A.

It seems like it should be a simple problem, but I'm lost.

Quote:

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Originally Posted by lovesmath

Suppose that A is contained in the set of all real numbers and is bounded above. Prove that if A contains one of its upper bounds, then this upper bound is sup A.

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Suppose that .

Now prove that .

Hint: If you assume that there is an intermediate contradiction.