Definition:Ring of Sequences/Pointwise Addition

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

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

 The operation $+’$ induced by $+$ on the ring of sequences is called pointwise addition and is defined as:
 * $\forall \sequence {x_n}, \sequence {y_n} \in R^{\N}: \sequence {x_n} +' \sequence {y_n} = \sequence {x_n + y_n}$

Also see

 * Definition:Pointwise Addition