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http://functions.wolfram.com/04.02.04.0006.01
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Limit[Ceiling[z - I \[Epsilon]], \[Epsilon] -> Plus[0]] == Ceiling[z] /;
Element[Im[z], Integers]
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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["Ceiling", "[", "z", "]"]]]], "/;", RowBox[List["Element", "[", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ",", "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> <munder> <mi> lim </mi> <mrow> <mi> ϵ </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mrow> <mo> + </mo> <mn> 0 </mn> </mrow> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mrow> <mo> ⌈ </mo> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> ϵ </mi> </mrow> </mrow> <mo> ⌉ </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mo> ⌈ </mo> <mi> z </mi> <mo> ⌉ </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <limit /> <bvar> <ci> ϵ </ci> </bvar> <condition> <apply> <tendsto /> <ci> ϵ </ci> <apply> <plus /> <cn type='integer'> 0 </cn> </apply> </apply> </condition> <apply> <ceiling /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> ϵ </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ceiling /> <ci> z </ci> </apply> </apply> <apply> <in /> <apply> <imaginary /> <ci> z </ci> </apply> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>
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| 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["Ceiling", "[", "z", "]"]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[Element]", "Integers"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
