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Suppose I wanted to say that

$x \in A \notin B$.

Is there a (better) standard way to describe this? Else, I'll go for my original formulation:

$ \ldots \text{where}\, x \in A\,\text{ but not in } B$

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    You could write $x \in A$, $x \notin B$. That's just a few symbols more...2012-11-10

3 Answers 3

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What you want is $x\in A\setminus B$: the set $A\setminus B$ is by definition the set of things that are in $A$ but not in $B$. (An older notation is $A-B$; I don’t recommend it.)

The expression $x\in A\notin B$ says something entirely different: it says that $x$ is an element of $A$, and $A$ is not an element of $B$.

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Your statement can be written with the set-minus character: $\setminus$

(For typesetting in LaTeX, for example, on math.se: use \setminus):

$x \in A\setminus B,$ which is defined to be exactly:

$x \in A \land x \notin B$

While you can chain together set inclusion $\subset$, e.g. $x \in A \subset B \subset C$ from which it follows that $x \in A \land x\in B \land x\in C$, that's not appropriate for set membership: $x \in A \notin B \not\equiv x \in A \land x \notin B.$

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    So, you suggested \setminus rather than -? +)2013-08-08
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Next formula describes your relation

$A \ni x \notin B$

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    Potentially, $\ni$ for reverse inclusion could be useful. For instance, if you want to sum over all sets $A$ containing $x$, you could write $\sum_{A \ni x} f(A)$. But I have to agree that $A \ni x \notin B$ is ugly...2012-11-11