Space of Bounded Sequences with Supremum Norm forms Normed Vector Space

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The vector space of bounded sequences with the supremum norm forms a normed vector space.


We have that:

Space of Bounded Sequences with Pointwise Addition and Pointwise Scalar Multiplication on Ring of Sequences forms Vector Space
Supremum norm on the space of bounded sequences is a norm

By definition, $\struct {\ell^\infty, \norm {\, \cdot \,}_\infty}$ is a normed vector space.