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I'm working through an academic game theory paper and stumbled upon this summation notation in a proof and I'm not quite sure what it means:

$\sum\limits_{j \in M \backslash\ \{i\}}$

There is a set $M$ indexed by $j$. There are other terms in the expression indexed by $i$. I'm curious what the $\backslash\{i\}$ means. Does this mean "with the exception of $i$"?

This context is an actor ($i$)'s utility function that depends on what other actors in the set $M$ do. Other actors are indexed by $j$.

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    Perfect, thanks so much!2012-04-22

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I'd translate the notation as "summation over all $j$'s such that $j \in M$ and $j \neq i$".

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Let X be a set and A be a subset of X, X\A = {x in X: x is not an element of A}.