Round[-z] == -Round[z]
Cell[BoxData[RowBox[List[RowBox[List["Round", "[", RowBox[List["-", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List["Round", "[", "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> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ⌉ </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mrow> <mo> ⌊ </mo> <mi> z </mi> <mo> ⌉ </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mo> ⌊ </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ⌉ </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mrow> <mo> ⌊ </mo> <mi> z </mi> <mo> ⌉ </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Round", "[", RowBox[List["-", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", RowBox[List["Round", "[", "z", "]"]]]]]]]]
2001-10-29