total ordering <mathematics> A {relation} R on a set A which is a {partial ordering]]; i.e. it is reflexive (xRx), transitive (xRyRz => xRz) and antisymmetric (xRyRx => x=y) and for any two elements x and y in A, either x R y or y R x. See also {equivalence relation}, {well-ordered}. (1995-02-16)