Examples of Ordered Fields
Examples of ordered fields are:
- the rational numbers
- the real algebraic numbers
- the computable numbers
- the real numbers
- the field of real rational functions, where p(x) and q(x), are polynomials with real coefficients, can be made into an ordered field where the polynomial p(x) = x is greater than any constant polynomial, by defining that whenever, for . This ordered field is not Archimedean.
- The field of formal Laurent series with real coefficients, where x is taken to be infinitesimal and positive
- real closed fields
- superreal numbers
- hyperreal numbers
The surreal numbers form a proper class rather than a set, but otherwise obey the axioms of an ordered field. Every ordered field can be embedded into the surreal numbers.
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