\begin{definition}[Definition:Ring of Sequences/Pointwise Addition]
Let $\struct {R, +, \circ}$ be a ring.
Let $\struct {R^\N, +', \circ'}$ be the ring of sequences over $R$.
<section notitle=true name=PointwiseAddition>
The pointwise operation $+'$ induced by $+$ on the ring of sequences is called '''pointwise addition''' and is defined as:
:$\forall \sequence {x_n}, \sequence {y_n} \in R^\N: \sequence {x_n} +' \sequence {y_n} = \sequence {x_n + y_n}$
</section>
\end{definition}