totally ordered

Adjective

 * 1)  That is equipped with a total order, that is a subset of (the ground set of) a partially ordered set whose partial order is a total order with respect to said subset.
 * 2) * 1976, K. D. Stroyan, W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, (Academic Press), page 67,
 * (A.2.5) THEOREM If A is a totally ordered ring and if I is a proper order ideal, then A/I is a totally ordered ring (with the operations and order given above).
 * 1) * 1996, Scientific Books staff (translators), Vasiliǐ M. Kopytov, Nikolaǐ Ya. Medvedev, Right-Ordered Groups, Scientific Books, page 98,
 * We introduce the following notation:
 * $$G$$ is a transitive group of order automorphisms of a totally ordered set $$X$$,
 * $$\theta$$ is a convex $$G$$-congruence on the totally ordered set $$X$$,
 * $$\xi$$ is the order type of the totally ordered set $$X$$,
 * $$\overline\eta$$ is the order type of some class $$Y=x\eta$$ of the congruence $$\eta$$,
 * $$\zeta$$ is the order type of the totally ordered quotient set $$X/\theta$$ of the totally ordered set $$X$$ by the congruence $$\theta$$.
 * $$\xi$$ is the order type of the totally ordered set $$X$$,
 * $$\overline\eta$$ is the order type of some class $$Y=x\eta$$ of the congruence $$\eta$$,
 * $$\zeta$$ is the order type of the totally ordered quotient set $$X/\theta$$ of the totally ordered set $$X$$ by the congruence $$\theta$$.

Translations

 * German: total geordnet