Proving the Intersection of Closed Sets is Closed | Homework Solution

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Homework Statement


Show that the intersection of two closed sets is closed.


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The Attempt at a Solution


Let X and Y be closed sets i.e. X and Y are equal to their closure X_ and Y_. Then X\capY is equal to X_\capY_.
 
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And how would that show X intersect Y is closed?
 

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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