DomainAndRange[Function[n, PartitionsP[n]]] == Integers?NonNegative \[LongRightArrow] Integers?Positive

Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List["n", ",", " ", RowBox[List["PartitionsP", "[", "n", "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["(", RowBox[List["Integers", "?", "NonNegative"]], ")"]], "\[LongRightArrow]", RowBox[List["Integers", "?", "Positive"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> n </mi> <mo> &#10230; </mo> <mrow> <semantics> <mi> p </mi> <annotation encoding='Mathematica'> TagBox[&quot;p&quot;, PartitionsP] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8759; </mo> <mrow> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> &#10230; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <ci> n </ci> <apply> <ci> PartitionsP </ci> <ci> n </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <integers /> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List["n_", ",", RowBox[List["PartitionsP", "[", "n_", "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Integers", "?", "NonNegative"]], "\[LongRightArrow]", RowBox[List["Integers", "?", "Positive"]]]]]]]]

2001-10-29