 The elements of a well-ordering \((A,\prec)\) can be divided into three types. Since A is non-empty there is least element with respect to \(\prec\) which is customarily denoted by 0 or \(0_A\). Then there are elements \(a\in A\) such that there exists \(b\prec a\) but there is no c between b and a. These are the successor elements of A, with a being the successor of b. An element \(c\in A\) such that \(0\prec c\) and for all \(b\prec c\) there exists \(d\in A\) with \(b\prec d\prec c\) is said to be a limit element of A.