Definition:Degree of Polynomial/Null Polynomial/Sequence

Definition
Let $f = \sequence {a_k} = \tuple {a_0, a_1, a_2, \ldots}$ be a polynomial over a field $F$.

Let $0_F$ be the zero of $F$.

Let $a_0 = a_1 = a_2 = \ldots = 0_F$.

Then $f$ is a null polynomial over $F$.