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 rationals. Examples of non-Archimedean are less simple.
