A metric is a mathematical generalization of the concept of distance between elements of a set (typically called points).
Definition (Metric) Formally, a metric \(d\) is a function on a space \(M\) where \(d:M\times M\to \mathbb{R}\) satisfying the following axioms for all points \(x,y,z\in M\): 1. \(d(x,x)=0\) 2. If \(x\neq y\) then \(d(x,y)>0\) 3. \(d(x,y)=d(y,x)\) (Symmetry) 4. \(d(x,z)\leq d(x,y)+d(y,z)\) (Triangle Inequality)