Question: If E = [0,1]' prove that supE = 1. PROOF. By the definition of interval, 1 is an upper bound of E. Let M be

If E = [0,1]' prove that supE = 1.

PROOF. By the definition of interval, 1 is an upper bound of E. Let M be any upper bound of E; Le., M ~ x for all x E E. Since 1 E E, it follows that M ~ 1.

Thus 1 is the smallest upper bound of E.

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