\begin{definition}[Definition:Field of Real Numbers]
The '''field of real numbers''' $\struct {\R, +, \times, \le}$ is the set of real numbers under the two operations of addition and multiplication, with an ordering $\le$ compatible with the ring structure of $\R$..
When the ordering $\le$ is subordinate or irrelevant in the context in which it is used, $\struct {\R, +, \times}$ is usually seen.
\end{definition}