Is the Closure of a Subset in l^{1} Compact?

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Homework Statement


Consider the Banach Space l^{1}. Let S={x \in l^{1}|\left\|x\right\|<1}. Is S a compact subset of l^{1}? prove or Disprove.
 
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S isn't even closed. A more interesting problem is whether the closure of S is compact, and I suspect this is what you're supposed to work on.
 

Thread 'Finding the nth roots of a complex number'

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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