Archimedean

A ring R is said to be Archimedean if the ring is ordered, has a metric and for all  in R, x non-zero, there exists  in the natural numbers such that . Here concatentation with  denotes adding  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.