Metric Space

A metric space ($\mathcal{M},d$) that satisfies:

1. $d:\mathcal{M}\times \mathcal{M}\to \mathbb{R}$
2. $d(x,x)=0$
3. If $x\ne y$ then $d(x,y)>0$
4. $d(x,y)=d(y,x)$
5. $d(x,z)\le d(x,y)+d(y,z)$