metric

Overview

This is a general way to describe the “distance” between points in a space. Many spaces come with their own metrics or with cannonical ones that are always used.

Definition

For a set X a metric is a function $d:X\times X\to \mathbb{R}$ such that

1. $d(x,y)\ge 0$ and equality only holds when $x=y$ (positive definite)
2. $d(x,y)=d(y,x)$ (symmetric)
3. Triangle inequality $d(x,y)+d(y,z)\ge d(x,z)$