ordered field

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.

Noun

  1. 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.

Forms

ordered fields

Hypernyms

field ordered integral domain

Hyponyms

real number system Archimedean ordered field Euclidean field