The function frac(x) giving the fractional (noninteger) part of a real number x. The symbol {x} is sometimes used instead of frac(x) (Graham et al. 1994, p. 70; Havil 2003, p. 109), but this notation is not used in this work due to possible confusion with the set containing the element x. Unfortunately, there is no universal agreement on the meaning of frac(x) for x<0 and there are two common definitions.
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