Limits of functions.

In this section we use the following notation:

$\displaystyle \overline{\mathbb{R}}=\mathbb{R} \cup \{ -\infty, +\infty \}.$    

A pointed neighborhood (or punctured neighborhood) of a real number $ x_0$ is a subset of $ \mathbb{R}$ of the form $ V-\{ x_0 \}$ , where $ V$ is a neighborhood of $ x_0$ in $ \mathbb{R}$ . For example, $ \mathbb{R}^*=\mathbb{R}-{0}$ is a punctured neighborhood of 0.

Noah Dana-Picard 2007-12-28