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## Homework Statement

Let [itex]\ell_\infty \mathbb({R})[/itex] be the set of bounded real sequences with k > 0 such that [itex]\left | x_n \right |\le k[/itex]

a) [itex](n)=(1,2,3...) \notin \ell_\infty \mathbb({R})[/itex]. This is not bounded 'above'?

b) [itex](2n^2+1) \notin \ell_\infty \mathbb({R})[/itex] Same answer as above?

c) [itex](1/n)=(1,1/2,1/3,1/4...) \in \ell_\infty \mathbb({R})[/itex] Is bounded above?

d) [itex](4-1/n) \notin \ell_\infty \mathbb({R})[/itex] Why is this not bounded? Is it because the value wll not go below 0?