Applying Cantor's diagonalization technique to sequences of functions

2 replies · 2K views · last reply
jdinatale
Messages
153
Reaction score
0
As usually, I type the problem and my attempt at the solution in LaTeX.

Applying Cantor's diagonalization technique to sequences of functions


Placeholder graphic reading "Photo not found. CLICK for Photos" with a camera icon, over a faded photo of a kitten with its mouth open.


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.

Applying Cantor's diagonalization technique to sequences of functions


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

Placeholder graphic reading "Photo not found. CLICK for Photos" over a blurred photo of a young kitten with its mouth open, and a camera icon below.