Let a > 0 and n >= 3 be an integer. Definethe set S = {x > 0 : x^n <= a}.

1. Show that S is bounded above and thus that b = sup S exists.

2. Show that b^n = a. To do this, show that it cannot be true that b^n < a or b^n > a.

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- October 26th 2008, 10:14 AMflamingBounded Set Question - Real Analysis
Let a > 0 and n >= 3 be an integer. Definethe set S = {x > 0 : x^n <= a}.

1. Show that S is bounded above and thus that b = sup S exists.

2. Show that b^n = a. To do this, show that it cannot be true that b^n < a or b^n > a.