Definition

Let $\struct {R, +, \circ}$ be a ring.

Let $\struct {R^\N, +', \circ'}$ be the ring of sequences over $R$.

The pointwise operation $+'$ induced by $+$ on the ring of sequences is called pointwise addition and is defined as:

$\forall \sequence {x_n}, \sequence {y_n} \in R^\N: \sequence {x_n} +' \sequence {y_n} = \sequence {x_n + y_n}$