\begin{definition}[Definition:Polynomial/Real Numbers]
A '''polynomial (in $\R$)''' is an expression of the form:
:$\ds \map P x = \sum_{j \mathop = 0}^n \paren {a_j x^j} = a_0 + a_1 x + a_2 x^2 + \cdots + a_{n - 1} x^{n - 1} + a_n x^n$
where:
:$x \in \R$
:$a_0, \ldots a_n \in \mathbb k$ where $\mathbb k$ is one of the standard number sets $\Z, \Q, \R$.
\end{definition}