/sci/ - Science & Math

This proof breaks even with the slightest amount of scrutiny. I do not understand how this proof made it into the book or was accepted by anyone.

This is extremely unclear what it means with k. n and k appears to be indexes, but since k is growing, it can't be considered a matrix...
So I suppose then, A_n,k is a collection of sets (I guess as it should).

But then it assumes that f(x) = lim fn(x), for x in A.
A_n,k is a subset of A.

if we fix an x, and we determine that f(x) = c, with an x in A, but not in A_n,k. Then fn(x) goes to infinity as n goes to infinity. Which is a contradiction and clearly breaks this proof.