# Archimedean

### From Conservapedia

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.