How can I show that if A > 0 and n is a positive, integer there is a positive number c such that c^n = A.

Here's my start for proving that c is a positive number

Let S be the set of all positive numbers x such that x^n < A. This set is not empty(how do I show this?). It is a bounded set and has a least upper bound(difficulty on proving ) which is c.

Then I have to prove that c^n = A.

If e > 0, there is some x in S s.t. c-e < x. hence (c-e)^n < A. Now let e -> 0 then c^n <= A. If c^n < A then I have prove this is not possible

I got this far... help !!