Recent content by math2006

Given a function f: [0,1] \to \mathbb{R}. Suppose f(x) = 0 if x is irrational and f(x) = 1/q if x = p/q, where p and q are relatively prime. Prove that f is Riemann integrable.

Let f be a real uniformly continuous function on the bounded set A in \mathbb{R}^1. Prove that f is bounded on A. Since f is uniformly continuous, take \epsilon = m, \exists \delta > 0 such that |f(x)-f(p)| < \epsilon whenever |x-p|<\delta and x,p \in A Now we have |f(x)| < m +...