Results 1 to 3 of 3

Math Help - Are periodic functions uniformly continuous?

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Are periodic functions uniformly continuous?

    I think it is, here is my proof:

    Suppose that f: \mathbb {R} \mapsto \mathbb {R} is a t-periodic function. We will show that f is uniformly continuous.

    Let  \epsilon > 0 , find  \delta > t such that  x \in \mathbb {R} with  y = x + t , then  |x-y| = | x - x + t | = |-t| = t < \delta

    We then have  |f(x) - f(y) | = |f(x) - f(x + t)| = |f(x)-f(x)| =0 < \epsilon , thus proves the claim.

    Is this right? Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by tttcomrader View Post
    Is this right?
    The statement is wrong how it is stated.
    Consider the sawtooth wave.
    Maybe you also had the condition that f is continous?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2
    It was a problem from a while back, so I do believe I missed the continuity part.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multiplication of uniformly continuous functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 3rd 2011, 07:02 AM
  2. Uniformly continuous functions
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: March 18th 2011, 09:04 AM
  3. Uniformly Continuous f and g functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 12th 2010, 10:02 PM
  4. Multiplying Uniformly Continuous functions
    Posted in the Differential Geometry Forum
    Replies: 9
    Last Post: March 25th 2010, 06:43 PM
  5. Replies: 3
    Last Post: October 20th 2008, 01:13 PM

Search Tags


/mathhelpforum @mathhelpforum