# Definition:Totally Ordered Field

## Definition

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

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

Let the ordering $\preceq$ be a total ordering.

Then $\left({F, +, \circ, \preceq}\right)$ is a totally ordered field.

## Also known as

This is often referred to as an ordered field.