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Everywhere, I have seen span of a set of vectors only. However, a vector space can also be taken as an infinite set of vectors following a particular rule. So can span be taken of a vector space (which will yield that very vector space only)?

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  • $\begingroup$ Yes, you can.$ $ $\endgroup$
    – Kenny Lau
    Sep 18, 2017 at 16:22
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    $\begingroup$ the span of any set is a collection of finite linear combination of the elements of that set. So you can define it for any subset of the vector space. In particular for $V$ also. $\endgroup$ Sep 18, 2017 at 16:26
  • $\begingroup$ @SachchidanandPrasad Why finite? I can have as many linear combinations as I want, using a field which is an infinite set? $\endgroup$ Sep 18, 2017 at 16:27
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    $\begingroup$ @ReeshabhRanjan In an arbitrary vector space how do you define infinite sum. Infinite sum is the limit of finite sum and for the limit concept you should have some distance notion. $\endgroup$ Sep 18, 2017 at 16:30

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