A distance function that satisfies all the below properties is called a metric
- non-negativity, \(d\left(x,y\right)\ge0\)
- isolation, \(d\left(x,y\right)=0\ \Leftrightarrow\ x=y\)
- symmetry, \(d\left(x,y\right)=d\left(y,x\right)\)
- triangle inequality ,\(d\left(x,z\right)\le d\left(x,y\right)+d\left(y,z\right)\)