Paper 2016 Solution

For each $n \ge 1$, let fn be a monotonic increasing real valued function on $[0, 1]$ such that the sequence of functions { $f_{n}$ } converges pointwise to the function $f \equiv 0$. Pick out the true statements from the following:
a. $ f_{n} $ converges to $f$ uniformly.
b. If the functions $ f_{n} $ are also non-negative, then $ f_{n} $ must be continuous for sufficiently large $n$.

For each $n \ge 1$, let fn be a monotonic increasing real valued function on $[0, 1]$ such that the sequence of functions ${fn}$ converges pointwise to the function f ≡ 0. Pick out the true statements from the following:
a. fn converges to f uniformly.
b. If the functions fn are also non-negative, then fn must be continuous for sufficiently large n.