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Give me some examples of basis for $\mathbb{R}$ (as vector space over field $k=\mathbb{Q}$).

Thanks.

  • 5
    The existence of such Hamel basis is ensured only by the AC(Axiom of Choice), and there seems no way to construct a concrete example of such a basis without reference to AC. I do not know much about this topic, but I believe that this is equivalent to some weaker formulation of AC. That is, the existence of a Hamel basis of $\mathbb{R}$ over $\mathbb{Q}$ is independent to ZF.2012-02-24
  • 3
    Please give me orders; I really enjoy being told what to do. Oh, wait. I *don't*. Never mind...2012-02-24

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