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 FractionalPart

 http://functions.wolfram.com/04.05.27.0024.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02