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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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Yes. This means "$j\in M$ and $j\neq i$". – Asaf Karagila Apr 22 '12 at 15:53
Perfect, thanks so much! – biased_estimator Apr 22 '12 at 15:55
up vote 1 down vote accepted

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}.

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