Does the definition of the linear span of a subset of a vector space require that the set be countable? – math.stackexchange.com

Does the definition of the linear span of a subset of a vector space require that the set be countable? – math.stackexchange.com

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My book gives this definition of linear span of a subset $S$ of a vector space $V$ : But when we write $k∈ℕ$, aren't we implying that $S$ is at most countable? That is, $S=${$v_i:i=1(1)k,k∈ℕ$}. But ...

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