Recent content by c1fn

  1. C

    Riemann Integrability of Thomae's Function

    Yes. That makes perfect sense. Thank you. Currently I'm working on showing fn → f uniformly.
  2. C

    Riemann Integrability of Thomae's Function

    Sorry I'm a bit confused when you say an enumeration of the rationals. Arn't the only rationals we're concerned about between 0 and 1? Can you elaborate a bit more on how you're defining f_n and what is a_1?
  3. C

    Riemann Integrability of Thomae's Function

    No I don't. I need to show this using uniform convergence (if that is possible).
  4. C

    Riemann Integrability of Thomae's Function

    Homework Statement Show the Thomae's function f : [0,1] → ℝ which is defined by f(x) = \begin{cases} \frac{1}{n}, & \text{if $x = \frac{m}{n}$, where $m, n \in \mathbb{N}$ and are relatively prime} \\ 0, & \text{otherwise} \end{cases} is Riemann integrable. Homework Equations Thm: If fn...