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## Homework Statement

Consider the normed linear space [itex]\ell_\infty \mathbb({R})[/itex]. Let [itex]x= \frac{n-1}{n}[/itex], [itex]y=(1/n) and z=2^n[/itex]

a) Are x,y,z each in [itex]\ell_\infty \mathbb({R})[/itex]

b) What is x+y? What is [itex]2^{1/2} y?[/itex]

c) Calculate [itex]||x||_\infty[/itex], [itex]||y||_\infty[/itex], [itex]||x+y||_\infty[/itex] and [itex]||2^{1/2} y ||_\infty[/itex]

For a) Does that mean are x,y,z subspaces of [itex]\ell_\infty \mathbb({R})[/itex]?