Definition:Ring of Sequences/Additive Inverse

Definition
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:
 * $\forall \sequence {x_n} \in R^{\N}: -\sequence {x_n} = \sequence {-x_n}$

Also see

 * Structure Induced by Ring Operations is Ring