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Consider the following statement which we denote S: For every $\\aleph_0$-coloring of the reals there exists distinct reals $e_1,e_2,e_3,e_4$ such that $e_1+e_2=e_3+e_4$?} Is it true? Erdos showed that S is equivalent to the negation of the Continuum Hypothesis, and hence S is indepedent of ZFC. 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