Let l∞ denote the vector space of all bounded sequences x = (x_n) of real numbers equipped with the norm

∥x∥ = sup |xn|. n∈N

Show that the set
Q={(an)∈l∞ :|an|≤2^(−n) forall n∈N}

is a compact subset of l∞.
Note: You may assume that l∞ is complete. You

may use whichever definition of compactness you find most convenient.

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