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

total ordering

    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)