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Round




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/04.03.04.0007.01









  


  








Input Form





Limit[Round[z + \[Epsilon]], \[Epsilon] -> Plus[0]] == Round[z] + 1 /; Element[(1/4) Re[2 z - 1], Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Round", "[", RowBox[List["z", "+", "\[Epsilon]"]], "]"]], ",", RowBox[List["\[Epsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Round", "[", "z", "]"]], "+", "1"]]]], "/;", RowBox[List["Element", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["Re", "[", RowBox[List[RowBox[List["2", " ", "z"]], "-", "1"]], "]"]]]], ",", "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> <mrow> <mo> &#8970; </mo> <mrow> <mi> z </mi> <mo> + </mo> <mi> &#1013; </mi> </mrow> <mo> &#8969; </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </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'> <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> <mrow> <mo> &#8970; </mo> <mrow> <mi> z </mi> <mo> + </mo> <mi> &#1013; </mi> </mrow> <mo> &#8969; </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Round", "[", RowBox[List["z_", "+", "\[Epsilon]_"]], "]"]], ",", RowBox[List["\[Epsilon]_", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Round", "[", "z", "]"]], "+", "1"]], "/;", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["Re", "[", RowBox[List[RowBox[List["2", " ", "z"]], "-", "1"]], "]"]]]], "\[Element]", "Integers"]]]]]]]]


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





2001-10-29