Show that the Thomass function is Riemann integrable, even though it is discontinuous at every rational number. HINT: For e > 0, there are only finitely many points taking values greater than e. Choose the options below that correctly explain why the Thomass function is Riemann integrable.
1) The Thomass function is continuous at every irrational number.
2) The Thomass function is bounded on any closed interval.
3) The Thomass function has a finite number of discontinuities.
4) The Thomass function is differentiable at every rational number.