Analysis: Infimum and Supremum

Rubik
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Homework Statement


Find the Supremum and Infimum of S where,
S = {(1/2n) : n is an integer, but not including 0}

Homework Equations


The Attempt at a Solution


Is it right if I got inf{S} = -∞ and sup{S} = ∞
 
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Try checking the values you obtain when substituting n=1,2,...:

{1/2,1/4,1/6,...}

Notice that your values are positive, so that, e.g., -5 is a lower bound. Notice too,

that all the values are smaller than, e.g. 10, so that 10 is an upper bound.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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