Is there a name for this relation: for all $x$ there is $y$ such that $xRy$, and for all $x,y,z$, if $xRy$ and $xRz$, then $y=z$? Suppose for all $x$ there is $y$ such that $xRy$, and for all $x,y,z$, if $xRy$ and $xRz$, then $y=z$.
Does there exist such a binary relation $R$ on some set such that the above properties are satisfied by $R$?

Define a relation $\operatorname{R}$ on $\Bbb{Z}$ such that  $x\operatorname{R}y$ if and only if  $x+y=0$,where '$+$' denotes the usual addition.
