Appendix: Hamel bases

Part of the Problem Books in Mathematics book series (PBM)


It would have been appropriate to mention Georg Hamel and his connection with the theory of functional equations in our historical survey of Chapter 1. However, the work of Hamel is technical, and best studied after a thorough analysis of Cauchy’s contributions such as in Chapter 2. I have seen fit to place Hamel’s work in this appendix because his contribution to the subject depends upon a highly speculative axiom in mathematics, namely the Axiom of Choice, which is not accepted by all mathematicians.


Real Number Functional Equation Rational Number Unique Representation Distinct Element 
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© Springer Science+Business Media, LLC 2007

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