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Proper summation notation 
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#1
Mar2712, 02:05 PM

P: 1,863

Hi
Is it correct of me to say that I want to carry out the sum [tex] \sum_i{v_iw_i} [/tex] where [itex]i\in\{x,y,z\}[/itex]? Or is it most correct to say that [itex]i=\{x,y,z\}[/itex]? Best regards, Niles. 


#2
Mar2712, 02:18 PM

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If you have the sum
[tex] v_x w_x + v_y w_y + v_z w_z[/tex] then you want [itex] i \in \{ x,y,z \} [/itex], which says sum over every element of the set [itex] \{x,y,z \}[/itex]. If you wrote [tex] \sum_{i=\{x,y,z \}} v_i w_i[/tex] what you really just wrote is [tex] v_{ \{x,y,z \}} w_{ \{x,y,z \}}[/tex] which is strange because it's not a sum, and because indices are unlikely (but might be) sets of variables 


#3
Mar2712, 02:20 PM

P: 1,863

Thanks, that is also what I thought was the case. I see the "i={x,y,z}"version in all sorts of books.
Best wishes, Niles. 


#4
Mar2712, 08:49 PM

P: 4,573

Proper summation notation
This is just my opinion, but the reason is mostly conventional because its easier for everyone with a simple mathematics background to understand and causes less confusion. 


#5
Mar2812, 02:19 AM

P: 1,863

Thanks for the help, that is kind of everybody.
Best, Niles. 


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