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Identifying a sequence as subset of subspace

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If I have some sequence $mathcal A = (a_i)$ of objects $a_i$ (maybe finite, maybe countably infinite) how can I say that those objects all exist in some subspace $S$? Is it correct to say $mathcal A subseteq S$? I’m not sure because $mathcal A$ isn’t a set it’s a sequence.


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