# Archimedean

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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.