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