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http://functions.wolfram.com/04.01.27.0013.01
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Floor[x] == Round[x - 1/2] + CharacteristicFunction[(x + 1)/2, Integers] /;
Element[x, Reals]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Floor", "[", "x", "]"]], "\[Equal]", RowBox[List[RowBox[List["Round", "[", RowBox[List["x", "-", FractionBox["1", "2"]]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox[RowBox[List["x", "+", "1"]], "2"], ",", "Integers"]], "]"]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> ⌊ </mo> <mi> x </mi> <mo> ⌋ </mo> </mrow> <mo> ⩵ </mo> <mtext> </mtext> <mrow> <mrow> <mo> ⌊ </mo> <mrow> <mi> x </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ⌉ </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> χ </mi> <mi> ℤ </mi> </msub> <mo> ( </mo> <mfrac> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mo> ⌊ </mo> <mi> x </mi> <mo> ⌋ </mo> </mrow> <mo> ⩵ </mo> <mtext> </mtext> <mrow> <mrow> <mo> ⌊ </mo> <mrow> <mi> x </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ⌉ </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> χ </mi> <mi> ℤ </mi> </msub> <mo> ( </mo> <mfrac> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Floor", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Round", "[", RowBox[List["x", "-", FractionBox["1", "2"]]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox[RowBox[List["x", "+", "1"]], "2"], ",", "Integers"]], "]"]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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