\begin{definition}[Definition:Ring of Sequences/Zero]
Let $\struct {R, +, \circ}$ be a ring.
Let $\struct {R^\N, +', \circ'}$ be the ring of sequences over $R$.
The zero of the ring of sequences is the constant sequence $\tuple {0, 0, 0, \dots}$, where $0$ is the zero of $R$.
\end{definition}