Meaning of totally ordered set

to'tally or'dered set'

Pronunciation: [key]
— Math. Math.
  1. a set in which a relation, as “less than or equal to,” holds for all pairs of elements of the set. Also called chain, linearly ordered set, simply ordered set. Cf. partially ordered set, well-ordered set.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.