Hamel Basis

A basis for the real numbers R, considered as a vector space over the rationals Q, i.e., a set of real numbers {U_alpha} such that every real number beta has a unique representation of the form

where r_i is rational and n depends on beta.

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.

See also

This entry contributed by Kevin O'Bryant

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O'Bryant, Kevin. "Hamel Basis." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HamelBasis.html

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