21. Hence the resulting field is an ordered field . 22. Similarly in the class of ordered fields , the existentially closed structures are the real closed fields. 23. Every subfield of an ordered field is also an ordered field ( inheriting the induced ordering ). 24. For an ordered field , Cauchy completeness is weaker than the other forms of completeness on this page. 25. Every subfield of an ordered field is also an ordered field ( inheriting the induced ordering ). 26. I'm not sure why the rational numbers don't count-by my understanding, they are a totally ordered field . 27. To assure his profits, Katzenberg wrote a letter that ordered Fields to be " an absolute killer ." 28. A court-ordered field test in March simulated aspects of the siege using heat-sensing FLIR, or forward-looking infrared, equipment. 29. Thus, an ordered field necessarily contains an infinite number of elements : a finite field cannot be ordered. 30. It can be shown that any ordered field , which is also complete, is isomorphic to the real numbers.
