#math/linear-algebra A function $p:F\to F$ is called a polynomial in F if there exists $a_{0}, \dots, a_{n}\in F$ such that $ p(z) = a_{0}+a_{1}z+\dots+a_{n}z^n $ for all $Z\in F$. We define $\mathcal{P}(F)$ as the set of all polynomials with coefficients in $F$. For a particular polynomial, the degree is defined as the largest $i$ where $a_{i}\neq{}0$. Then, $\mathcal{P}_{m}(F)$ is the set of all polynomials, $p$, where deg $p=m$. - $\mathcal{P}_{m}(F)=$ span$(1, z, \dots, z^m)$ where $z^k=f_{k}(x)=x^k$ for all $x \in F$. - The 0 polynomial has degree $-\infty$.