Definition 2
Tag 06Z2, permanent. Cite it as [Bourbaki, Tag 06Z2].
Algebra, chapter VI, § 2. Ordered fields
— A commutative field, equipped with a total ordering, is called an ordered field if its ordering and its ring structure are compatible.
We restrict ourselves to total order relations on fields because the others are very « pathological » (VI, p. 38, Ex. 6).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.