Ceiling[z] == -Floor[-z]
Cell[BoxData[RowBox[List[RowBox[List["Ceiling", "[", "z", "]"]], "\[Equal]", RowBox[List["-", RowBox[List["Floor", "[", RowBox[List["-", "z"]], "]"]]]]]]]]
<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> <mo> - </mo> <mrow> <mo> ⌊ </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ⌋ </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ceiling /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Ceiling", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", RowBox[List["Floor", "[", RowBox[List["-", "z"]], "]"]]]]]]]]
2007-05-02
){kind=small}
