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 FractionalPart

 http://functions.wolfram.com/04.05.27.0020.01

 Input Form

 FractionalPart[x] == x - Ceiling[x] + 1 - Sign[UnitStep[-x] + CharacteristicFunction[-x, Integers]] /; Element[x, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["FractionalPart", "[", "x", "]"]], "\[Equal]", RowBox[List["x", "-", RowBox[List["Ceiling", "[", "x", "]"]], "+", "1", "-", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["-", "x"]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["-", "x"]], ",", "Integers"]], "]"]]]], "]"]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]

 MathML Form

 frac ( x ) x - x - sgn ( χ ( - x ) + θ ( - x ) ) + 1 /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] Condition FractionalPart x x -1 x -1 Sign Subscript χ -1 x θ -1 x 1 x [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FractionalPart", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", "-", RowBox[List["Ceiling", "[", "x", "]"]], "+", "1", "-", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["-", "x"]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["-", "x"]], ",", "Integers"]], "]"]]]], "]"]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02