Applying Cantor's diagonalization technique to sequences of functions

[jdinatale]

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

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.

Would I need to do induction on two variables? (m and k)

 

[jdinatale]

Bump. This stuff is only undergraduate analysis, I know someone can help.

 

[jdinatale]

I think I might have it, let me know what you guys think: