On Uniform Convergence

1. Aug 6, 2007

dracond

1. The problem statement, all variables and given/known data

Just trying to get feel for uniform convergence and it's relationship to boundedness. If a sequence of functions (fn) converges uniformly to f and (fn) is a sequence of bounded functions, is f also bounded?

2. Relevant equations

3. The attempt at a solution

2. Aug 6, 2007

Dick

If the convergence is uniform then for all e there is an N such that |fn(x)-f(x)|<e for all n>=N. If fN is bounded and f unbounded, how can this be?

Last edited: Aug 6, 2007