Aligning symbols underneath each other neatly












2















I'm trying to align the equal and greater than signs underneath each other but can't seem to get them aligned properly (see image attached). How can I align them correctly? I have included my lines of code below.



enter image description here



begin{equation}
begin{aligned}
Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big] = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \

geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \

= maxBig{h_i(X_i^{j_1...j_i}),Ebig[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \

geq maxBig{h_i(X_i^{j_1...j_i}),Ebig[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \

= V_ibig(X_i^{j_1...j_i}big).
end{aligned}
end{equation}









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  • 1





    welcome to tex.se! please extend your code fragment to complete small document with your equation.

    – Zarko
    4 hours ago






  • 3





    Welcome to tex.sx. Since you're using aligned, you should place an & just before the relation (= or geq); that is the alignment point you are looking for. The user guide for the amsmath package provides clear instructions for this and other math structures.

    – barbara beeton
    4 hours ago













  • If you're not interested in numbering the equation, use align*. Also, there's max instead of max, together with , dots, instead of ....

    – Werner
    4 hours ago











  • Off-topic: all-blank lines are not legal syntax if the amsmath package is loaded (which is the case here, since you're employing an aligned environment).

    – Mico
    3 hours ago
















2















I'm trying to align the equal and greater than signs underneath each other but can't seem to get them aligned properly (see image attached). How can I align them correctly? I have included my lines of code below.



enter image description here



begin{equation}
begin{aligned}
Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big] = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \

geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \

= maxBig{h_i(X_i^{j_1...j_i}),Ebig[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \

geq maxBig{h_i(X_i^{j_1...j_i}),Ebig[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \

= V_ibig(X_i^{j_1...j_i}big).
end{aligned}
end{equation}









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  • 1





    welcome to tex.se! please extend your code fragment to complete small document with your equation.

    – Zarko
    4 hours ago






  • 3





    Welcome to tex.sx. Since you're using aligned, you should place an & just before the relation (= or geq); that is the alignment point you are looking for. The user guide for the amsmath package provides clear instructions for this and other math structures.

    – barbara beeton
    4 hours ago













  • If you're not interested in numbering the equation, use align*. Also, there's max instead of max, together with , dots, instead of ....

    – Werner
    4 hours ago











  • Off-topic: all-blank lines are not legal syntax if the amsmath package is loaded (which is the case here, since you're employing an aligned environment).

    – Mico
    3 hours ago














2












2








2








I'm trying to align the equal and greater than signs underneath each other but can't seem to get them aligned properly (see image attached). How can I align them correctly? I have included my lines of code below.



enter image description here



begin{equation}
begin{aligned}
Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big] = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \

geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \

= maxBig{h_i(X_i^{j_1...j_i}),Ebig[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \

geq maxBig{h_i(X_i^{j_1...j_i}),Ebig[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \

= V_ibig(X_i^{j_1...j_i}big).
end{aligned}
end{equation}









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maths student is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












I'm trying to align the equal and greater than signs underneath each other but can't seem to get them aligned properly (see image attached). How can I align them correctly? I have included my lines of code below.



enter image description here



begin{equation}
begin{aligned}
Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big] = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \

geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \

= maxBig{h_i(X_i^{j_1...j_i}),Ebig[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \

geq maxBig{h_i(X_i^{j_1...j_i}),Ebig[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \

= V_ibig(X_i^{j_1...j_i}big).
end{aligned}
end{equation}






equations vertical-alignment






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edited 4 hours ago









Phelype Oleinik

23.6k54586




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asked 4 hours ago









maths studentmaths student

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maths student is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






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Check out our Code of Conduct.








  • 1





    welcome to tex.se! please extend your code fragment to complete small document with your equation.

    – Zarko
    4 hours ago






  • 3





    Welcome to tex.sx. Since you're using aligned, you should place an & just before the relation (= or geq); that is the alignment point you are looking for. The user guide for the amsmath package provides clear instructions for this and other math structures.

    – barbara beeton
    4 hours ago













  • If you're not interested in numbering the equation, use align*. Also, there's max instead of max, together with , dots, instead of ....

    – Werner
    4 hours ago











  • Off-topic: all-blank lines are not legal syntax if the amsmath package is loaded (which is the case here, since you're employing an aligned environment).

    – Mico
    3 hours ago














  • 1





    welcome to tex.se! please extend your code fragment to complete small document with your equation.

    – Zarko
    4 hours ago






  • 3





    Welcome to tex.sx. Since you're using aligned, you should place an & just before the relation (= or geq); that is the alignment point you are looking for. The user guide for the amsmath package provides clear instructions for this and other math structures.

    – barbara beeton
    4 hours ago













  • If you're not interested in numbering the equation, use align*. Also, there's max instead of max, together with , dots, instead of ....

    – Werner
    4 hours ago











  • Off-topic: all-blank lines are not legal syntax if the amsmath package is loaded (which is the case here, since you're employing an aligned environment).

    – Mico
    3 hours ago








1




1





welcome to tex.se! please extend your code fragment to complete small document with your equation.

– Zarko
4 hours ago





welcome to tex.se! please extend your code fragment to complete small document with your equation.

– Zarko
4 hours ago




3




3





Welcome to tex.sx. Since you're using aligned, you should place an & just before the relation (= or geq); that is the alignment point you are looking for. The user guide for the amsmath package provides clear instructions for this and other math structures.

– barbara beeton
4 hours ago







Welcome to tex.sx. Since you're using aligned, you should place an & just before the relation (= or geq); that is the alignment point you are looking for. The user guide for the amsmath package provides clear instructions for this and other math structures.

– barbara beeton
4 hours ago















If you're not interested in numbering the equation, use align*. Also, there's max instead of max, together with , dots, instead of ....

– Werner
4 hours ago





If you're not interested in numbering the equation, use align*. Also, there's max instead of max, together with , dots, instead of ....

– Werner
4 hours ago













Off-topic: all-blank lines are not legal syntax if the amsmath package is loaded (which is the case here, since you're employing an aligned environment).

– Mico
3 hours ago





Off-topic: all-blank lines are not legal syntax if the amsmath package is loaded (which is the case here, since you're employing an aligned environment).

– Mico
3 hours ago










3 Answers
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In addition to providing & alignments points in five places, you should also (a) write max instead of max and (b) use large | symbols (by writing bigmvert and biggmvert). Do please replace all instances of ... with dots. I would also like to suggest that you use upright-E letters to denote the expectations operator. Do write bigl( and bigr), etc rather than just big( and big); that way, the spacing around the opening and closing "fence" symbols can be optimized by LaTeX. Last but not least, don't over-size the fence symbols; e.g., don't write Biggl[ when biggl[ does just as well -- or, arguably, even better!



enter image description here



documentclass{article}
usepackage{amsmath}
DeclareMathOperator{E}{E}
begin{document}

begin{equation}
begin{aligned}
Ebigl[,widehat{V}_i^{j_1dots j_i}bigmvert X_i^{j_1dots j_i}bigr]
&= Ebiggl[maxbiggl{h_i(X_i^{j_1dots j_i}),frac{1}{b}sum_{j=1}^{b}
widehat{V}_{i+1}^{j_1dots j_ij}biggr} biggmvert X_i^{j_1dots j_i}biggr] \
&ge maxbiggl{h_i(X_i^{j_1dots j_i}),Ebiggl[frac{1}{b}sum_{j=1}^{b}
widehat{V}_{i+1}^{j_1dots j_ij}biggmvert X_i^{j_1dots j_i}biggr]biggr} \
&= maxbigl{h_i(X_i^{j_1dots j_i}),Ebigl[,widehat{V}_{i+1}^{j_1dots j_ij}
bigmvert X_i^{j_1dots j_i}bigr]bigr} \
&ge maxbigl{h_i(X_i^{j_1dots j_i}),
Ebigl[,V_{i+1}bigl(X_{i+1}^{j_1dots j_i1}bigr)
bigmvert X_i^{j_1dots j_i}bigr] bigr} \
&= V_ibigl(X_i^{j_1dots j_i}bigr),.
end{aligned}
end{equation}
end{document}





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    2














    you forgot on ampersands ... and max is probably operator max:



    documentclass{article}
    usepackage{mathtools}

    begin{document}
    begin{equation}
    begin{aligned}
    Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big]
    & = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b}
    widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \
    & geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b}
    widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \
    & = maxBig{h_i(X_i^{j_1...j_i}),E
    big[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \
    & geq maxBig{h_i(X_i^{j_1...j_i}),E
    big[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \
    & = V_ibig(X_i^{j_1...j_i}big).
    end{aligned}
    end{equation}
    end{document}


    enter image description here






    share|improve this answer































      1














      Another solution with DeclarePairedDelimiter and its variants, from mathtools: this allows us to declare the E and Set command which can take an optional argument, chosen in big, Big, bigg, Bigg, which implicitly adds a pair of bigl ... bigr, &c., around the delimiters. Alternatively, there is a star version, which adds a pair of left ... right. Furthermore, the vertical line is translated into a given command, which adapts its size to the delimiters size. Note that in the first two lines, I used smaller delimiters, which I thought more convenient.



      documentclass{article}
      usepackage[utf8]{inputenc}%
      usepackage{mathtools}

      providecommandgiven{}

      DeclarePairedDelimiterXPPE[1]{mathrm E}{}{%
      renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
      #1}
      DeclarePairedDelimiterXSet[1]{}{%
      renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
      #1}
      begin{document}

      begin{equation}
      begin{aligned}
      E[big]{widehat{V}_i^{j_1...j_i}given X_i^{j_1...j_i}} & = E[bigg]{maxSet[bigg]{{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}}given X_i^{j_1...j_i}} \
      & geq maxSet[bigg]{h_i(X_i^{j_1...j_i}), E[bigg]{frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
      & = maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
      & geq maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{V_{i+1}bigl(X_{i+1}^{j_1...j_i1}bigr)given X_i^{j_1...j_i}}} \
      & = V_ibigl(X_i^{j_1...j_i}bigr).
      end{aligned}
      end{equation}

      end{document}


      enter image description here






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        3 Answers
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        3 Answers
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        3














        In addition to providing & alignments points in five places, you should also (a) write max instead of max and (b) use large | symbols (by writing bigmvert and biggmvert). Do please replace all instances of ... with dots. I would also like to suggest that you use upright-E letters to denote the expectations operator. Do write bigl( and bigr), etc rather than just big( and big); that way, the spacing around the opening and closing "fence" symbols can be optimized by LaTeX. Last but not least, don't over-size the fence symbols; e.g., don't write Biggl[ when biggl[ does just as well -- or, arguably, even better!



        enter image description here



        documentclass{article}
        usepackage{amsmath}
        DeclareMathOperator{E}{E}
        begin{document}

        begin{equation}
        begin{aligned}
        Ebigl[,widehat{V}_i^{j_1dots j_i}bigmvert X_i^{j_1dots j_i}bigr]
        &= Ebiggl[maxbiggl{h_i(X_i^{j_1dots j_i}),frac{1}{b}sum_{j=1}^{b}
        widehat{V}_{i+1}^{j_1dots j_ij}biggr} biggmvert X_i^{j_1dots j_i}biggr] \
        &ge maxbiggl{h_i(X_i^{j_1dots j_i}),Ebiggl[frac{1}{b}sum_{j=1}^{b}
        widehat{V}_{i+1}^{j_1dots j_ij}biggmvert X_i^{j_1dots j_i}biggr]biggr} \
        &= maxbigl{h_i(X_i^{j_1dots j_i}),Ebigl[,widehat{V}_{i+1}^{j_1dots j_ij}
        bigmvert X_i^{j_1dots j_i}bigr]bigr} \
        &ge maxbigl{h_i(X_i^{j_1dots j_i}),
        Ebigl[,V_{i+1}bigl(X_{i+1}^{j_1dots j_i1}bigr)
        bigmvert X_i^{j_1dots j_i}bigr] bigr} \
        &= V_ibigl(X_i^{j_1dots j_i}bigr),.
        end{aligned}
        end{equation}
        end{document}





        share|improve this answer






























          3














          In addition to providing & alignments points in five places, you should also (a) write max instead of max and (b) use large | symbols (by writing bigmvert and biggmvert). Do please replace all instances of ... with dots. I would also like to suggest that you use upright-E letters to denote the expectations operator. Do write bigl( and bigr), etc rather than just big( and big); that way, the spacing around the opening and closing "fence" symbols can be optimized by LaTeX. Last but not least, don't over-size the fence symbols; e.g., don't write Biggl[ when biggl[ does just as well -- or, arguably, even better!



          enter image description here



          documentclass{article}
          usepackage{amsmath}
          DeclareMathOperator{E}{E}
          begin{document}

          begin{equation}
          begin{aligned}
          Ebigl[,widehat{V}_i^{j_1dots j_i}bigmvert X_i^{j_1dots j_i}bigr]
          &= Ebiggl[maxbiggl{h_i(X_i^{j_1dots j_i}),frac{1}{b}sum_{j=1}^{b}
          widehat{V}_{i+1}^{j_1dots j_ij}biggr} biggmvert X_i^{j_1dots j_i}biggr] \
          &ge maxbiggl{h_i(X_i^{j_1dots j_i}),Ebiggl[frac{1}{b}sum_{j=1}^{b}
          widehat{V}_{i+1}^{j_1dots j_ij}biggmvert X_i^{j_1dots j_i}biggr]biggr} \
          &= maxbigl{h_i(X_i^{j_1dots j_i}),Ebigl[,widehat{V}_{i+1}^{j_1dots j_ij}
          bigmvert X_i^{j_1dots j_i}bigr]bigr} \
          &ge maxbigl{h_i(X_i^{j_1dots j_i}),
          Ebigl[,V_{i+1}bigl(X_{i+1}^{j_1dots j_i1}bigr)
          bigmvert X_i^{j_1dots j_i}bigr] bigr} \
          &= V_ibigl(X_i^{j_1dots j_i}bigr),.
          end{aligned}
          end{equation}
          end{document}





          share|improve this answer




























            3












            3








            3







            In addition to providing & alignments points in five places, you should also (a) write max instead of max and (b) use large | symbols (by writing bigmvert and biggmvert). Do please replace all instances of ... with dots. I would also like to suggest that you use upright-E letters to denote the expectations operator. Do write bigl( and bigr), etc rather than just big( and big); that way, the spacing around the opening and closing "fence" symbols can be optimized by LaTeX. Last but not least, don't over-size the fence symbols; e.g., don't write Biggl[ when biggl[ does just as well -- or, arguably, even better!



            enter image description here



            documentclass{article}
            usepackage{amsmath}
            DeclareMathOperator{E}{E}
            begin{document}

            begin{equation}
            begin{aligned}
            Ebigl[,widehat{V}_i^{j_1dots j_i}bigmvert X_i^{j_1dots j_i}bigr]
            &= Ebiggl[maxbiggl{h_i(X_i^{j_1dots j_i}),frac{1}{b}sum_{j=1}^{b}
            widehat{V}_{i+1}^{j_1dots j_ij}biggr} biggmvert X_i^{j_1dots j_i}biggr] \
            &ge maxbiggl{h_i(X_i^{j_1dots j_i}),Ebiggl[frac{1}{b}sum_{j=1}^{b}
            widehat{V}_{i+1}^{j_1dots j_ij}biggmvert X_i^{j_1dots j_i}biggr]biggr} \
            &= maxbigl{h_i(X_i^{j_1dots j_i}),Ebigl[,widehat{V}_{i+1}^{j_1dots j_ij}
            bigmvert X_i^{j_1dots j_i}bigr]bigr} \
            &ge maxbigl{h_i(X_i^{j_1dots j_i}),
            Ebigl[,V_{i+1}bigl(X_{i+1}^{j_1dots j_i1}bigr)
            bigmvert X_i^{j_1dots j_i}bigr] bigr} \
            &= V_ibigl(X_i^{j_1dots j_i}bigr),.
            end{aligned}
            end{equation}
            end{document}





            share|improve this answer















            In addition to providing & alignments points in five places, you should also (a) write max instead of max and (b) use large | symbols (by writing bigmvert and biggmvert). Do please replace all instances of ... with dots. I would also like to suggest that you use upright-E letters to denote the expectations operator. Do write bigl( and bigr), etc rather than just big( and big); that way, the spacing around the opening and closing "fence" symbols can be optimized by LaTeX. Last but not least, don't over-size the fence symbols; e.g., don't write Biggl[ when biggl[ does just as well -- or, arguably, even better!



            enter image description here



            documentclass{article}
            usepackage{amsmath}
            DeclareMathOperator{E}{E}
            begin{document}

            begin{equation}
            begin{aligned}
            Ebigl[,widehat{V}_i^{j_1dots j_i}bigmvert X_i^{j_1dots j_i}bigr]
            &= Ebiggl[maxbiggl{h_i(X_i^{j_1dots j_i}),frac{1}{b}sum_{j=1}^{b}
            widehat{V}_{i+1}^{j_1dots j_ij}biggr} biggmvert X_i^{j_1dots j_i}biggr] \
            &ge maxbiggl{h_i(X_i^{j_1dots j_i}),Ebiggl[frac{1}{b}sum_{j=1}^{b}
            widehat{V}_{i+1}^{j_1dots j_ij}biggmvert X_i^{j_1dots j_i}biggr]biggr} \
            &= maxbigl{h_i(X_i^{j_1dots j_i}),Ebigl[,widehat{V}_{i+1}^{j_1dots j_ij}
            bigmvert X_i^{j_1dots j_i}bigr]bigr} \
            &ge maxbigl{h_i(X_i^{j_1dots j_i}),
            Ebigl[,V_{i+1}bigl(X_{i+1}^{j_1dots j_i1}bigr)
            bigmvert X_i^{j_1dots j_i}bigr] bigr} \
            &= V_ibigl(X_i^{j_1dots j_i}bigr),.
            end{aligned}
            end{equation}
            end{document}






            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 3 hours ago

























            answered 4 hours ago









            MicoMico

            280k31384772




            280k31384772























                2














                you forgot on ampersands ... and max is probably operator max:



                documentclass{article}
                usepackage{mathtools}

                begin{document}
                begin{equation}
                begin{aligned}
                Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big]
                & = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b}
                widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \
                & geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b}
                widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \
                & = maxBig{h_i(X_i^{j_1...j_i}),E
                big[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \
                & geq maxBig{h_i(X_i^{j_1...j_i}),E
                big[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \
                & = V_ibig(X_i^{j_1...j_i}big).
                end{aligned}
                end{equation}
                end{document}


                enter image description here






                share|improve this answer




























                  2














                  you forgot on ampersands ... and max is probably operator max:



                  documentclass{article}
                  usepackage{mathtools}

                  begin{document}
                  begin{equation}
                  begin{aligned}
                  Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big]
                  & = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b}
                  widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \
                  & geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b}
                  widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \
                  & = maxBig{h_i(X_i^{j_1...j_i}),E
                  big[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \
                  & geq maxBig{h_i(X_i^{j_1...j_i}),E
                  big[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \
                  & = V_ibig(X_i^{j_1...j_i}big).
                  end{aligned}
                  end{equation}
                  end{document}


                  enter image description here






                  share|improve this answer


























                    2












                    2








                    2







                    you forgot on ampersands ... and max is probably operator max:



                    documentclass{article}
                    usepackage{mathtools}

                    begin{document}
                    begin{equation}
                    begin{aligned}
                    Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big]
                    & = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b}
                    widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \
                    & geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b}
                    widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \
                    & = maxBig{h_i(X_i^{j_1...j_i}),E
                    big[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \
                    & geq maxBig{h_i(X_i^{j_1...j_i}),E
                    big[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \
                    & = V_ibig(X_i^{j_1...j_i}big).
                    end{aligned}
                    end{equation}
                    end{document}


                    enter image description here






                    share|improve this answer













                    you forgot on ampersands ... and max is probably operator max:



                    documentclass{article}
                    usepackage{mathtools}

                    begin{document}
                    begin{equation}
                    begin{aligned}
                    Ebig[widehat{V}_i^{j_1...j_i}|X_i^{j_1...j_i}big]
                    & = EBigg[maxBigg{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b}
                    widehat{V}_{i+1}^{j_1...j_ij}Bigg}|X_i^{j_1...j_i}Bigg] \
                    & geq maxBigg{h_i(X_i^{j_1...j_i}),EBigg[frac{1}{b}sum_{j=1}^{b}
                    widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}Bigg]Bigg} \
                    & = maxBig{h_i(X_i^{j_1...j_i}),E
                    big[widehat{V}_{i+1}^{j_1...j_ij}|X_i^{j_1...j_i}big]Big} \
                    & geq maxBig{h_i(X_i^{j_1...j_i}),E
                    big[V_{i+1}big(X_{i+1}^{j_1...j_i1}big)|X_i^{j_1...j_i}big]Big} \
                    & = V_ibig(X_i^{j_1...j_i}big).
                    end{aligned}
                    end{equation}
                    end{document}


                    enter image description here







                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered 4 hours ago









                    ZarkoZarko

                    126k867164




                    126k867164























                        1














                        Another solution with DeclarePairedDelimiter and its variants, from mathtools: this allows us to declare the E and Set command which can take an optional argument, chosen in big, Big, bigg, Bigg, which implicitly adds a pair of bigl ... bigr, &c., around the delimiters. Alternatively, there is a star version, which adds a pair of left ... right. Furthermore, the vertical line is translated into a given command, which adapts its size to the delimiters size. Note that in the first two lines, I used smaller delimiters, which I thought more convenient.



                        documentclass{article}
                        usepackage[utf8]{inputenc}%
                        usepackage{mathtools}

                        providecommandgiven{}

                        DeclarePairedDelimiterXPPE[1]{mathrm E}{}{%
                        renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
                        #1}
                        DeclarePairedDelimiterXSet[1]{}{%
                        renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
                        #1}
                        begin{document}

                        begin{equation}
                        begin{aligned}
                        E[big]{widehat{V}_i^{j_1...j_i}given X_i^{j_1...j_i}} & = E[bigg]{maxSet[bigg]{{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}}given X_i^{j_1...j_i}} \
                        & geq maxSet[bigg]{h_i(X_i^{j_1...j_i}), E[bigg]{frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
                        & = maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
                        & geq maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{V_{i+1}bigl(X_{i+1}^{j_1...j_i1}bigr)given X_i^{j_1...j_i}}} \
                        & = V_ibigl(X_i^{j_1...j_i}bigr).
                        end{aligned}
                        end{equation}

                        end{document}


                        enter image description here






                        share|improve this answer




























                          1














                          Another solution with DeclarePairedDelimiter and its variants, from mathtools: this allows us to declare the E and Set command which can take an optional argument, chosen in big, Big, bigg, Bigg, which implicitly adds a pair of bigl ... bigr, &c., around the delimiters. Alternatively, there is a star version, which adds a pair of left ... right. Furthermore, the vertical line is translated into a given command, which adapts its size to the delimiters size. Note that in the first two lines, I used smaller delimiters, which I thought more convenient.



                          documentclass{article}
                          usepackage[utf8]{inputenc}%
                          usepackage{mathtools}

                          providecommandgiven{}

                          DeclarePairedDelimiterXPPE[1]{mathrm E}{}{%
                          renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
                          #1}
                          DeclarePairedDelimiterXSet[1]{}{%
                          renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
                          #1}
                          begin{document}

                          begin{equation}
                          begin{aligned}
                          E[big]{widehat{V}_i^{j_1...j_i}given X_i^{j_1...j_i}} & = E[bigg]{maxSet[bigg]{{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}}given X_i^{j_1...j_i}} \
                          & geq maxSet[bigg]{h_i(X_i^{j_1...j_i}), E[bigg]{frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
                          & = maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
                          & geq maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{V_{i+1}bigl(X_{i+1}^{j_1...j_i1}bigr)given X_i^{j_1...j_i}}} \
                          & = V_ibigl(X_i^{j_1...j_i}bigr).
                          end{aligned}
                          end{equation}

                          end{document}


                          enter image description here






                          share|improve this answer


























                            1












                            1








                            1







                            Another solution with DeclarePairedDelimiter and its variants, from mathtools: this allows us to declare the E and Set command which can take an optional argument, chosen in big, Big, bigg, Bigg, which implicitly adds a pair of bigl ... bigr, &c., around the delimiters. Alternatively, there is a star version, which adds a pair of left ... right. Furthermore, the vertical line is translated into a given command, which adapts its size to the delimiters size. Note that in the first two lines, I used smaller delimiters, which I thought more convenient.



                            documentclass{article}
                            usepackage[utf8]{inputenc}%
                            usepackage{mathtools}

                            providecommandgiven{}

                            DeclarePairedDelimiterXPPE[1]{mathrm E}{}{%
                            renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
                            #1}
                            DeclarePairedDelimiterXSet[1]{}{%
                            renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
                            #1}
                            begin{document}

                            begin{equation}
                            begin{aligned}
                            E[big]{widehat{V}_i^{j_1...j_i}given X_i^{j_1...j_i}} & = E[bigg]{maxSet[bigg]{{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}}given X_i^{j_1...j_i}} \
                            & geq maxSet[bigg]{h_i(X_i^{j_1...j_i}), E[bigg]{frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
                            & = maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
                            & geq maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{V_{i+1}bigl(X_{i+1}^{j_1...j_i1}bigr)given X_i^{j_1...j_i}}} \
                            & = V_ibigl(X_i^{j_1...j_i}bigr).
                            end{aligned}
                            end{equation}

                            end{document}


                            enter image description here






                            share|improve this answer













                            Another solution with DeclarePairedDelimiter and its variants, from mathtools: this allows us to declare the E and Set command which can take an optional argument, chosen in big, Big, bigg, Bigg, which implicitly adds a pair of bigl ... bigr, &c., around the delimiters. Alternatively, there is a star version, which adds a pair of left ... right. Furthermore, the vertical line is translated into a given command, which adapts its size to the delimiters size. Note that in the first two lines, I used smaller delimiters, which I thought more convenient.



                            documentclass{article}
                            usepackage[utf8]{inputenc}%
                            usepackage{mathtools}

                            providecommandgiven{}

                            DeclarePairedDelimiterXPPE[1]{mathrm E}{}{%
                            renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
                            #1}
                            DeclarePairedDelimiterXSet[1]{}{%
                            renewcommandgiven{nonscript:delimsizevertnonscript:mathopen{}}
                            #1}
                            begin{document}

                            begin{equation}
                            begin{aligned}
                            E[big]{widehat{V}_i^{j_1...j_i}given X_i^{j_1...j_i}} & = E[bigg]{maxSet[bigg]{{h_i(X_i^{j_1...j_i}),frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}}given X_i^{j_1...j_i}} \
                            & geq maxSet[bigg]{h_i(X_i^{j_1...j_i}), E[bigg]{frac{1}{b}sum_{j=1}^{b} widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
                            & = maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{widehat{V}_{i+1}^{j_1...j_ij}given X_i^{j_1...j_i}}} \
                            & geq maxSet[Big]{h_i(X_i^{j_1...j_i}),E[big]{V_{i+1}bigl(X_{i+1}^{j_1...j_i1}bigr)given X_i^{j_1...j_i}}} \
                            & = V_ibigl(X_i^{j_1...j_i}bigr).
                            end{aligned}
                            end{equation}

                            end{document}


                            enter image description here







                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered 3 hours ago









                            BernardBernard

                            171k775203




                            171k775203






















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