Ceiling function: Representations through equivalent functions (formula 04.02.27.0006)

Ceiling

$Mathematica Notation$

Integer Functions

Ceiling[z]

Representations through equivalent functions

With related functions

With Mod

http://functions.wolfram.com/04.02.27.0006.01

Input Form

Ceiling[z] == z + Mod[-z, 1]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Ceiling", "[", "z", "]"]], "\[Equal]", RowBox[List["z", "+", RowBox[List["Mod", "[", RowBox[List[RowBox[List["-", "z"]], ",", "1"]], "]"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ⌈ </mo> <mi> z </mi> <mo> ⌉ </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> z </mi> <mo> + </mo> <semantics> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 1 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> $CellContext`z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </annotation-xml> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ceiling /> <ci> z </ci> </apply> <apply> <plus /> <ci> z </ci> <apply> <rem /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> $CellContext`z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Ceiling", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", "+", RowBox[List["Mod", "[", RowBox[List[RowBox[List["-", "z"]], ",", "1"]], "]"]]]]]]]]

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

2001-10-29