# The discrete metric is defined as \(d_0:E\times E\rightarrow \mathbb{R}\) such that

The discrete metric is defined as \(d_0:E\times E\rightarrow \mathbb{R}\) such that

\(d_0(x,y)=\left{\begin{array}{rcl} 1,&\mbox{if}&x\neq y\\-1,&\mbox{if}&x=y\end{array}\right\)

—>> \(d_0(x,y)=\left{\begin{array}{rcl}1,&\mbox{if}&x\neq y\\0,&\mbox{if}&x=y\end{array}\right\)

\(d_0(x,y)=\left{\begin{array}{rcl}0,&\mbox{if}&x\neq y\\-1,&\mbox{if}&x=y\end{array}\right\)

\(d_0(x,y)=\left{\begin{array}{rcl}1,&\mbox{if}&x\geq y\\-1,&\mbox{if}&x\leq y\end{array}\right\)