Difference between revisions of "Archimedean"
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Latest revision as of 21:24, 7 November 2011
A ring R is said to be Archimedean if the ring is ordered, has a metric and for all in R, x nonzero, 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 nonArchimedean are less simple.