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 FractionalPart

 http://functions.wolfram.com/04.05.02.0001.01

 Input Form

 FractionalPart[x] == x - n /; Element[x, Reals] && Element[n, Integers] && Inequality[0, LessEqual, Sign[x] (x - n), Less, 1] && x != 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["FractionalPart", "[", "x", "]"]], "\[Equal]", RowBox[List["x", "-", "n"]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["0", "\[LessEqual]", RowBox[List[RowBox[List["Sign", "[", "x", "]"]], RowBox[List["(", RowBox[List["x", "-", "n"]], ")"]]]], "<", "1"]], "\[And]", RowBox[List["x", "\[NotEqual]", "0"]]]]]]]]

 MathML Form

 frac ( x ) x - n /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] 0 sgn ( x ) ( x - n ) < 1 x 0 Condition FractionalPart x x -1 n x n Inequality 0 Sign x x -1 n 1 x 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FractionalPart", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", "-", "n"]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["0", "\[LessEqual]", RowBox[List[RowBox[List["Sign", "[", "x", "]"]], " ", RowBox[List["(", RowBox[List["x", "-", "n"]], ")"]]]], "<", "1"]], "&&", RowBox[List["x", "\[NotEqual]", "0"]]]]]]]]]]

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

 2001-10-29