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:
“The case of Andrews is really a very bad one, as appears by the record already before me. Yet before receiving this I had ordered his punishment commuted to imprisonment ... and had so telegraphed. I did this, not on any merit in the case, but because I am trying to evade the butchering business lately.”
—Abraham Lincoln (1809–1865)
“It is through attentive love, the ability to ask “What are you going through?” and the ability to hear the answer that the reality of the child is both created and respected.”
—Mary Field Belenky (20th century)