An ordered field is a field F together with a positive cone P.
The preorderings on F are precisely the intersections of families of positive cones on F. The positive cones are the maximal preorderings.
Read more about Ordered Field: Properties of Ordered Fields, Examples of Ordered Fields, Which Fields Can Be Ordered?, Topology Induced By The Order, Harrison Topology
Famous quotes containing the words ordered and/or field:
“But one sound always rose above the clamor of busy life and, no matter how much of a tintinnabulation, was never confused and, for a moment lifted everything into an ordered sphere: that of the bells.”
—Johan Huizinga (1872–1945)
“The field of the poor may yield much food, but it is swept away through injustice.”
—Bible: Hebrew, Proverbs 13:23.