Applying Cantor's diagonalization technique to sequences of functions

jdinatale
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As usually, I type the problem and my attempt at the solution in LaTeX.

6214a.png


6214b.png


Ok, so for the last part (c), I obviously have the diagram down, now I just have to construct the nested sequence of functions that converges at every point in A. I drew a diagram to help illustrate the idea.

picture.jpg


Would I need to do induction on two variables? (m and k)
 
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Bump. This stuff is only undergraduate analysis, I know someone can help.
 
I think I might have it, let me know what you guys think:

dat.png
 

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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