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 FractionalPart

 http://functions.wolfram.com/04.05.27.0016.01

 Input Form

 FractionalPart[x] == x - Round[x - 1/2] - 1 /; (Element[x, Reals] && x < 0) || Element[(x + 1)/2, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["FractionalPart", "[", "x", "]"]], "\[Equal]", RowBox[List["x", "-", RowBox[List["Round", "[", RowBox[List["x", "-", FractionBox["1", "2"]]], "]"]], "-", "1"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["x", "<", "0"]]]], "\[Or]", RowBox[List[FractionBox[RowBox[List["x", "+", "1"]], "2"], "\[Element]", "Integers"]]]]]]]]

 MathML Form

 frac ( x ) x - x - 1 2 - 1 /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] x < 0 x + 1 2 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] frac ( x ) x - x - 1 2 - 1 /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] x < 0 x + 1 2 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FractionalPart", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", "-", RowBox[List["Round", "[", RowBox[List["x", "-", FractionBox["1", "2"]]], "]"]], "-", "1"]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", "<", "0"]]]], ")"]], "||", RowBox[List[FractionBox[RowBox[List["x", "+", "1"]], "2"], "\[Element]", "Integers"]]]]]]]]]]

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

 2007-05-02