An ordered field is a field 
equipped with a total order 
that is compatible with addition
and multiplication. Thus 
implies 
,
and 
and 
imply 
. The rational numbers
and real numbers are ordered fields, whereas the complex numbers admit no compatible field ordering.
Ordered Field
See also
Field, Total OrderExplore with Wolfram|Alpha
References
Lang, S. Algebra, 3rd ed. New York: Springer-Verlag, 2002.Cite this as:
Weisstein, Eric W. "Ordered Field." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OrderedField.html