\begin{definition}[Definition:Ring of Sequences/Additive Inverse]
Let $\struct {R, +, \circ}$ be a ring.
Let $\struct {R^\N, +', \circ'}$ be the ring of sequences over $R$.
From Structure Induced by Ring Operations is Ring, $\struct {R^\N, +', \circ'}$ is a ring.
The additive inverse in the ring of sequences is defined by:
:$\forall \sequence {x_n} \in R^\N: -\sequence {x_n} = \sequence {-x_n}$
\end{definition}