User:IssaRice/Stringing together relations and binary operations

If $R$ is a relation on a set $X$, and $x,y,z$ are elements of $X$, we sometimes write $x\mathrel {R} y\mathrel {R} z$ as an abbreviation of "$x\mathrel {R} y$ and $y\mathrel {R} z$. This makes sense especially when $R$ is a transitive relation, because in that case we also have $x\mathrel {R} z$, which is suggested by the notation "$x\mathrel {R} y\mathrel {R} z$".

For instance, if we have three real numbers $x,y,z$ and the relation $\leq$, then $x\leq y\leq z$ means that $x\leq y$ and $y\leq z$. Since the relation is transitive, we also have $x\leq z$.