n. 1. the order axiom for the real line that states that if a and b are real numbers such that a < b/n for all natural numbers n then a ≤ 0, or equivalently, that for any positive a and b there is a positive integer n such that a < nb, and thus that every real number is less than some natural number. This is equivalent to the assertion that the real numbers are conditionally complete. An infinitesimal is non-Archimedean as it is less than any positive non-zero number. See also cofinal, dense, non-standard analysis. 2. the corresponding property of a partial order on an ordered vector space. This fails in the lexical order on Euclidean 2-space.