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An ordered field F is said to be a complete ordered field iff every nonempty subset S of F which is bounded above has a supremum, or least upper bound, in F.
The real numbers are an example of a complete ordered field, while the rational numbers are not (To see that the rationals are not a complete ordered field, consider the subset S := { rational numbers q such that q*q < 2 }. It is not difficult to see that the least upper bound of this subset is sqrt(2), which is not a rational number.)

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