1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: On Uniform Convergence

  1. Aug 6, 2007 #1
    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. jcsd
  3. Aug 6, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook