## ORDEREDFIELD

### Ordered field

In mathematics, an**ordered field**is a field together with a total ordering of its elements that is compatible with the field operations. Historically, the axiomatization of an ordered field was abstracted gradually from the real numbers, by mathematicians including David Hilbert, Otto HĂ¶lder and Hans Hahn. In 1926, this grew eventually into the Artinâ€“Schreier theory of ordered fields and formally real fields.

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### ordered field

#### Noun

- A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides.

*The above text is a snippet from Wiktionary: ordered field*

and as such is available under the Creative Commons Attribution/Share-Alike License.

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