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Date: 17-6-2021
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A basis for the real numbers , considered as a vector space over the rationals , i.e., a set of real numbers such that every real number has a unique representation of the form
where is rational and depends on .
The axiom of choice is equivalent to the statement: "Every vector space has a vector space basis," and this is the only justification for the existence of a Hamel basis.
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