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Erdos and Graham found it conceivable that the best n-term Egyptian underapproximation of almost every positive number for sufficiently large n gets constructed in a greedy manner, i. e. , from the best (n-1) -term Egyptian underapproximation. We show that the opposite is true: the set of real numbers with this property has Lebesgue measure zero. This note solves Problem 206 on Bloom's website "Erdos problems".
Vjekoslav Kovač (Tue,) studied this question.