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Ceiling




Mathematica Notation

Traditional Notation









Integer Functions > Ceiling[z] > General characteristics > Sets of discontinuity





http://functions.wolfram.com/04.02.04.0007.01









  


  








Input Form





Limit[Ceiling[z + I \[Epsilon]], \[Epsilon] -> Plus[0]] == Ceiling[z] + I /; Element[Im[z], Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Ceiling", "[", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]"]]]], "]"]], ",", RowBox[List["\[Epsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "\[Equal]", " ", RowBox[List[RowBox[List["Ceiling", "[", "z", "]"]], "+", "\[ImaginaryI]"]]]], "/;", RowBox[List["Element", "[", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ",", "Integers"]], "]"]]]]]]








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> <munder> <mi> lim </mi> <mrow> <mi> &#1013; </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mrow> <mo> + </mo> <mn> 0 </mn> </mrow> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8968; </mo> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#1013; </mi> </mrow> </mrow> <mo> &#8969; </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> &#8968; </mo> <mi> z </mi> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <limit /> <bvar> <ci> &#1013; </ci> </bvar> <condition> <apply> <tendsto /> <ci> &#1013; </ci> <apply> <plus /> <cn type='integer'> 0 </cn> </apply> </apply> </condition> <apply> <ceiling /> <apply> <plus /> <ci> z </ci> <apply> <times /> <imaginaryi /> <ci> &#1013; </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ceiling /> <ci> z </ci> </apply> <imaginaryi /> </apply> </apply> <apply> <in /> <apply> <imaginary /> <ci> z </ci> </apply> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Ceiling", "[", RowBox[List["z_", "+", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]_"]]]], "]"]], ",", RowBox[List["\[Epsilon]_", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", "z", "]"]], "+", "\[ImaginaryI]"]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[Element]", "Integers"]]]]]]]]


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





2001-10-29