A ring R is said to be Archimedean if the ring is ordered, has a metric | | and for all x,y in R, x non-zero, there exists n in the natural numbers such that n | x | > y. Here concatentation with n denotes adding n times. Informally, a ring is Archimedean if it has no infinitely small or infinitely large elements. Examples of Archimedean rings include the real numbers and the rational numbers. Examples of non-Archimedean are less simple.