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## Homework Statement

a) Prove that [itex]\ell_\infty \mathbb({R})[/itex] is a subspace of [itex]\ell \mathbb({R})

[/itex]

b) Show that [itex]\left \| \right \|_\infty[/itex] is a norm on [itex]\ell_\infty (\mathbb{R})[/itex]

## The Attempt at a Solution

For a) I guess we have to show that [itex]\vec{x} + \vec{y} \in \ell_\infty \mathbb({R})[/itex] and [itex]\alpha \vec({x}) \in \ell_\infty \mathbb({R})[/itex]

but I don't know how to proceed...thanks

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