Definition:Totally Ordered Field

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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.


Also see


Sources