We say that a function h:**R**-->**R** is a Hamel
function (h \in HF) if h, considered as a subset of **R**^{2}, is
a Hamel basis for **R**^{2}. We prove that
every function from **R** into **R** can be
represented as a pointwise sum of two Hamel functions.
The latter is equivalent to the statement: for all
f_{1},f_{2}:**R**-->**R**
there is a
g:**R**-->**R**
such that g+f_{1} and g+f_{2} are in HF. We show that this
fails for infinitely many functions.

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**Last modified November 8, 2001.**