Archimedean field - Revision history

Vipul: /* Relation with other properties */

2009-05-14T22:01:23Z

Relation with other properties

← Older revision		Revision as of 22:01, 14 May 2009
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	===Weaker properties===		===Weaker properties===

	* [[Stronger than::Formally real field]]		* [[Stronger than::Formally real field]]: {{proofofstrictimplicationat\|[[Archimedean implies formally real]]\|[[Formally real not implies Archimedean]]}}
	* [[Stronger than::Field of characteristic zero]]		* [[Stronger than::Field of characteristic zero]]

			===Incomparable properties===

			* [[Euclidean field]]
			* [[Pythagorean field]]

2009-05-14T22:00:25Z

← Older revision		Revision as of 22:00, 14 May 2009
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	==Definition==		==Definition==

			===In terms of a subfield of the reals===

			An '''Archimedean field''' is a [[field]] that is isomorphic to a [[subfield]] of the [[field of real numbers]].

			===In terms of a total ordering===
	An '''Archimedean field''' is a [[field]] with a total ordering <math>\le</math> on its elements satisfying the following:		An '''Archimedean field''' is a [[field]] with a total ordering <math>\le</math> on its elements satisfying the following:

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	==Relation with other properties==		==Relation with other properties==

	~~===Stronger properties===~~

	* [[Weaker than::Totally real field]]

	===Weaker properties===		===Weaker properties===