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Q49Section II (Mathematics)49 of 180

Analysis — subsets of ℓ∞\ell^\infty: every option fails

Let B be the collection of bounded real sequences with sup norm ∥⋅∥∞\|\cdot\|_\infty. Let A0={{xn}:xn=0∀n≥10}A_0=\{\{x_n\}:x_n=0 \forall n\ge10\} and B0={{xn}:∥{xn}∥∞≤1}B_0=\{\{x_n\}:\|\{x_n\}\|_\infty\le1\}. Then:

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