Results 1 to 4 of 4

Math Help - Continuous Function proof

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    5

    Continuous Function proof

    Prove that the function f defined by f(x)=x if x is rational and f(x)=-x if x is irrational is continuous at 0 only.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1596
    Awards
    1
    Quote Originally Posted by redsoxnation View Post
    Prove that the function f defined by f(x)=x if x is rational and f(x)=-x if x is irrational is continuous at 0 only.
    Because this is not a homework service, you need to show us some effort on your part.
    We will happily give you help on what you have already done.
    But do not expect us to do your work for you.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    17
    Quote Originally Posted by redsoxnation View Post
    Prove that the function f defined by f(x)=x if x is rational and f(x)=-x if x is irrational is continuous at 0 only.
    Hint: If f is indeed continuous, then f^{-1}( (0,1) ) is a non-empty open subset of R. It also contains 1/2, for instance. Since 1/2 lies in an open subset of R, look at an irrational number in a neighborhood of 1/2 and show that it doesn't map into (0,1) as originally assumed.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by redsoxnation View Post
    Prove that the function f defined by f(x)=x if x is rational and f(x)=-x if x is irrational is continuous at 0 only.
    I DO NOT want to do your HW for you...Plato is right, show us some work. But, a hint that may be easier than patrick is to consider that f is continuous implies that x_n\to x\implies f(x_n)\to f(x)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof for Continuous function
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: March 30th 2010, 10:42 PM
  2. help with continuous function proof
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 21st 2008, 01:26 PM
  3. continuous function proof
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 5th 2007, 12:26 PM
  4. Continuous Function Proof 2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 14th 2007, 10:58 PM
  5. Continuous Function Proof
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 13th 2007, 04:16 PM

Search Tags


/mathhelpforum @mathhelpforum