In mathematics, a well-order relation (or well-ordering) on a set S's a total order on S with the property that every non-empty subset of S has a least element in this ordering.Equivalently, a well-ordering's a well-founded total order. The set S together with the well-order relation's then called a well-ordered set. Every element s, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all elements greater than s. Every subset whic… (More on Well-order)