Exercise 1, § 2

Show that on the real line $\mathbf{R}$ (with the additive uniformity) the function $|x|$ is uniformly continuous; the function $1/x$ is uniformly continuous in every interval $[a, +\infty[$ where $a > 0$; and that this function is continuous, but not uniformly continuous, in the interval $]0, +\infty[$.*