If $X$ is a Set and $<$ is an Ordering on $X$, and if $a<b$, we use the notation $(a,b)$ to denote the set

$\{x |a<x<b\}$;

it is called an Open interval in $X$. If this set is empty, we call $a$ the Immediate predecessor of $b$, and we call $b$ the Immediate successor of $a$