# Definition:Degree of Polynomial/Sequence

## Definition

### Ring

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

The degree of $f$ is defined as the largest $n \in \Z$ such that $a_n \ne 0$.

### Field

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

The degree of $f$ is defined as the largest $n \in \Z$ such that $a_n \ne 0$.