In mathematics, specifically in order theory, a binary relation ≤ {\displaystyle \,\leq \,} on a vector space X {\displaystyle X} over the real or complex numbers is called Archimedean if for all x ∈ X , {\displaystyle x\in X,} whenever there exists some y ∈ X {\displaystyle y\in X} such that n x ≤ y {\displaystyle nx\leq y} for all positive integers n , {\displaystyle n,} then necessarily x ≤ 0. {\displaystyle x\leq 0.} An Archimedean (pre)ordered vector space is a (pre)ordered vector space whose order is Archimedean. A preordered vector space X {\displaystyle X} is called almost Archimedean if for all x ∈ X , {\displaystyle x\in X,} whenever there exists a y ∈ X {\displaystyle y\in X} such that − n − 1 y ≤ x ≤ n − 1 y {\displaystyle -n^{-1}y\leq x\leq n^{-1}y} for all positive integers n , {\displaystyle n,} then x = 0. {\displaystyle x=0.}