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http://functions.wolfram.com/04.02.16.0020.01
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Ceiling[Ceiling[n x]/n] == Ceiling[x] /; Element[x, Reals] &&
Element[n, Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", FractionBox[RowBox[List["Ceiling", "[", RowBox[List["n", " ", "x"]], "]"]], "n"], "]"]], "\[Equal]", RowBox[List["Ceiling", "[", "x", "]"]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]
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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> <mfrac> <mrow> <mo> ⌈ </mo> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mi> x </mi> </mrow> <mo> ⌉ </mo> </mrow> <mi> n </mi> </mfrac> <mo> ⌉ </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> ⌈ </mo> <mi> x </mi> <mo> ⌉ </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ceiling /> <apply> <times /> <apply> <ceiling /> <apply> <times /> <ci> n </ci> <ci> x </ci> </apply> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ceiling /> <ci> x </ci> </apply> </apply> <apply> <and /> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Ceiling", "[", FractionBox[RowBox[List["Ceiling", "[", RowBox[List["n_", " ", "x_"]], "]"]], "n_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Ceiling", "[", "x", "]"]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
