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Real number (view source)

Revision as of 00:54, March 10, 2008

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==Formal definition==

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Formally, real numbers are defined as the unique [[Field (mathematics)|field]] which is [[ordered]], [[Complete (mathematics)|complete]], and [[Archimedean]]. The reals can be constructed from the rationals by means of [[Dedekind cut]]s or [[Cauchy sequence]]s, i.e. it is the completion of the [[metric space]] of rational numbers.

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Formally, real numbers are defined as the unique [[Field (mathematics)|field]] which is [[ordered]], [[Complete (mathematics)|complete]], and [[Archimedean]]. The reals can be constructed from the [[rationals]] by means of [[Dedekind cut]]s or [[Cauchy sequence]]s, i.e. it is the completion of the [[metric space]] of rational numbers.

==Infinity==

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