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Math Help - Infinite dimensional vector space bases.

  1. #1
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    Infinite dimensional vector space bases.

    Here is a question I was wondering. It seems it should be true, but I can't figure it out.

    Let V be an \mathbb{R}-vector space and let S \subset V be a nonempty subset of V. Let W be the vector space generated by S. Does S contain a basis for W?

    I am aware that this is trivial if V is finite-dimensional, but what about in the infinite-dimensional case? I have the feeling that it requires the axiom of choice.
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  2. #2
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    Re: Infinite dimensional vector space bases.

    Update: I managed to do it using Zorn's lemma, essentially following the proof at PlanetMath with a few minor changes to the proof.
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