- #1

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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.

- Thread starter Niles
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- #1

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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

Office_Shredder

Staff Emeritus

Science Advisor

Gold Member

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[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

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Best wishes,

Niles.

- #4

chiro

Science Advisor

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While one can interpret that, it would make more sense if associated an index set with your label set if you need to do this. So if instead of {x,y,z} just introduce the bijection {x,y,z} = {1,2,3} where the ith component of one set maps to the ith of the other.

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.

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.

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Thanks for the help, that is kind of everybody.

Best,

Niles.

Best,

Niles.

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