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Math Help - Finding a Hamel base.

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    Finding a Hamel base.

    Let X be a non-empty set, and let \mathcal{\mathcal{H}} be the set of functions \mathcal{H}=\left\{ f\,:\, X\rightarrow\mathbb{C}:\, f(x)=0\text{ for all but a finite number of points } x\in X\right\} equipped with the usual pointwise vector operations. For each f\in\mathcal{H}, define the subset S(f) of X by S(f)=\left\{ x\in X\::\: f(x)\neq0\right\}
    Exhibit an explicit Hamel base for \mathcal{H}, showing that it satisfies all the requirements of such a base.
    Last edited by Opalg; February 21st 2010 at 01:40 AM. Reason: Fixed LaTeX
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