Definition:Ring of Sequences/Additive Inverse
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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:
- $\forall \sequence {x_n} \in R^\N: -\sequence {x_n} = \sequence {-x_n}$