Min[Subscript[x, 1], Subscript[x, 2]] == (1/2) (Subscript[x, 1] + Subscript[x, 2] - Sqrt[(Subscript[x, 1] - Subscript[x, 2])^2]) /; Element[Subscript[x, 1], Reals] && Element[Subscript[x, 2], Reals]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Min", "[", RowBox[List[SubscriptBox["x", "1"], " ", ",", SubscriptBox["x", "2"]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SubscriptBox["x", "1"], "+", SubscriptBox["x", "2"], "-", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["x", "1"], "-", SubscriptBox["x", "2"]]], ")"]], "2"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["x", "1"], "\[Element]", "Reals"]], " ", "\[And]", " ", RowBox[List[SubscriptBox["x", "2"], "\[Element]", "Reals"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> min </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msqrt> <msup> <mrow> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <min /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <reals /> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Min", "[", RowBox[List[SubscriptBox["x_", "1"], ",", SubscriptBox["x_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SubscriptBox["xx", "1"], "+", SubscriptBox["xx", "2"], "-", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["xx", "1"], "-", SubscriptBox["xx", "2"]]], ")"]], "2"]]]], ")"]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["xx", "1"], "\[Element]", "Reals"]], "&&", RowBox[List[SubscriptBox["xx", "2"], "\[Element]", "Reals"]]]]]]]]]]

2001-10-29