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Ceiling




Mathematica Notation

Traditional Notation









Integer Functions > Ceiling[z] > Primary definition





http://functions.wolfram.com/04.02.02.0001.01









  


  








Input Form





Ceiling[x] == n /; Element[x, Reals] && Element[n, Integers] && Inequality[n - 1, Less, x, LessEqual, n]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", "x", "]"]], "\[Equal]", "n"]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["n", "-", "1"]], "<", "x", "\[LessEqual]", "n"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8968; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> <mo> &#10869; </mo> <mi> n </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <mi> x </mi> <mo> &#8804; </mo> <mi> n </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ceiling /> <ci> x </ci> </apply> <ci> n </ci> </apply> <apply> <and /> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> <apply> <ci> Inequality </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <lt /> <ci> x </ci> <leq /> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Ceiling", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["n", "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["n", "-", "1"]], "<", "x", "\[LessEqual]", "n"]]]]]]]]]]


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





2001-10-29