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 (18091865)
“They talk about a womans sphere,
As though it had a limit.
Theres not a place in earth or heaven.
Theres not a task to mankind given ...
Without a woman in it.”
—Kate Field (18381896)