Definition:Totally Ordered Field

Definition

Let $\left({F, +, \circ, \preceq}\right)$ be an ordered field.

If the ordering $\preceq$ is a total ordering, then $\left({F, +, \circ, \preceq}\right)$ is a totally ordered field.

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 23$