The Free On-line Dictionary of Computing (30 December 2018):

total orderingA 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)