Results 1 to 2 of 2

Math Help - Continuous Functions

  1. #1
    Member
    Joined
    Jul 2009
    Posts
    168

    Continuous Functions

    Let:

    f(x)=\left\{\begin{matrix} \frac{1}{q}, & \mbox{if }x\mbox{ is rational}  \\ 0, & \mbox{if }x\mbox{ is irrational}<br />
 \end{matrix}\right.

    while: q>0, x=\frac{p}{q} , and p,q are relatively prime.

    How can I prove that f is continuous in every irrational point, and noncontinuous in rational points?

    It looks as if it is not continuous at all (because between every irrational number there's a rational number, and vice-verse)

    *(Sorry for my bad English)

    Can anyone please help me to find a way to solve this problem?

    Thank you very much
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2010
    Posts
    354
    This seems to explain this function in great detail:

    Thomae's function - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Continuous functions
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: July 12th 2011, 12:23 PM
  2. [SOLVED] Continuous Functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 22nd 2011, 11:07 AM
  3. Continuous Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 24th 2010, 02:02 AM
  4. Continuous Functions!
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 20th 2010, 01:02 PM
  5. Continuous functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 1st 2009, 11:48 AM

Search Tags


/mathhelpforum @mathhelpforum