Prerequisites

Abstract

We denote by $\mathbb R ^n$ the set of points with n real coordinates. In this text we will often represent functions abstractly by saying how many numbers go into the function and how many come out. So, if we write $f:\mathbb{R}^n \to \mathbb{R}^{m},$ we mean f is a function whose input is a point with n coordinates and whose output is a point with m coordinates.