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 Round

 http://functions.wolfram.com/04.03.27.0025.01

 Input Form

 Round[x] == Quotient[x + 1/2, 1] - CharacteristicFunction[(2 x - 1)/4, Integers] /; Element[x, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Round", "[", "x", "]"]], "\[Equal]", RowBox[List[RowBox[List["Quotient", "[", RowBox[List[RowBox[List["x", "+", FractionBox["1", "2"]]], ",", "1"]], "]"]], "-", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", "x"]], "-", "1"]], "4"], ",", "Integers"]], "]"]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]

 MathML Form

 x quotient ( x + 1 2 , 1 ) - χ ( 2 x - 1 4 ) /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] x quotient ( x + 1 2 , 1 ) - χ ( 2 x - 1 4 ) /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Round", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Quotient", "[", RowBox[List[RowBox[List["x", "+", FractionBox["1", "2"]]], ",", "1"]], "]"]], "-", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "x"]], "-", "1"]], ")"]]]], ",", "Integers"]], "]"]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]

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

 2007-05-02