# Thread: Real Analysis - Uniform Conv

1. ## Real Analysis - Uniform Conv

If fn --> f uniformly on a set A, and if fn --> f uniformly on a set B, then fn --> f uniformly on A U B.

This is the last question I need to answer. I can't really figure it out because there's nothing similar to this question in the book's examples.

2. ## Idea

I think the answer is false, but I can't think of a viable counterexample.

3. Originally Posted by ajj86
If fn --> f uniformly on a set A, and if fn --> f uniformly on a set B, then fn --> f uniformly on A U B.
You have an integer $N_A$ to use with set $A$.
You have an integer $N_B$ to use with set $B$.
If $N=N_A + N_B$ would that work on $A \cup B$?
Why or why not?