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$
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$
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 $B$.
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: $x \in A \notin B \not\equiv x \in A \land x \notin B.$
Next formula describes your relation
$A \ni x \notin B$