ordered field in a sentence

Examples

1. Every other ordered field can be embedded in the surreals.
2. Every ordered field can be embedded into the surreal numbers.
3. Every Squares are necessarily non-negative in an ordered field.
4. Taking rational functions with rational instead of real coefficients produces a countable non-Archimedean ordered field.
5. The surreal numbers form a set, but otherwise obey the axioms of an ordered field.
6. We've gotten pretty close to an ordered field by now, but we're not quite there.
7. Formally, we say that the complex numbers cannot have the structure of an ordered field.
8. More generally, the substructures of an ordered field ( or just a group are its subgroups.
9. This provides a connection between surreal numbers and more conventional mathematical approaches to ordered field theory.
10. Every ordered field is a formally real field.