Meaning of totally ordered | Babel Free

Definitions

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.

not-comparable

Equivalents

Examples

“1976, K. D. Stroyan, W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Harcourt Brace Jovanovich (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).”

“The set {1, 2, 3, 4, 6, 8, 12, 24}, ordered by 'divides' is not totally ordered, since (for example) 6 and 8 are not related. However, the set {1, 2, 4, 12, 24} is totally ordered by the relation 'divides'.”

“G is a transitive group of order automorphisms of a totally ordered set X, θ is a convex G-congruence on the totally ordered set X, ξ is the order type of the totally ordered set X, ◌̅η is the order type of some class Y=xη of the congruence η,”

CEFR level