How Do You Prove A Closure Equals A Union Boundary A?

Virtate
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How do you do this proof? Isn't it already obvious given the definition? I have no idea how to go about writing it down. :confused: If someone could help me with this, I would really appreciate it. Thanks :) Sorry I had to write it in such a messy way.

Define the closure of A as A closure = (x|for every open rectangle u containing x, intersection of u and A not equal to 0)

a) Show that A closure = A union bdA

b) Prove that bdA = intersection of A closure and (R^n-A) closure = bd(R^n-A)
 
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Can we see your proof before we answer?
 
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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