Quick Maths grammar question - How to write a domain of $x$? A function $f(x) = k$ and the domain is $\{-2,-1,\dotsc,3\}$. Would I say 
$$x = \{-2,-1,\dotsc,3\}\quad\text{or}\quad x \in \{-2,-1,\dotsc,3\} \ ?$$
Thanks. 
 A: Your second alternative is the correct one.
The value of $x$ is not a set of numbers, rather it is in a set of numbers.
A: Here's one way to look at it:
When you write $x = \lbrace -2, -1, \dotsc ,3\rbrace$ you are saying "$x$ is equal to the set consisting of the integers $-2$ through $3$".  If $x$ were really a set then you'd be fine, but if you want to say that the set consists of the possible values for $x$, that is it's the domain of $f$, then saying $x = \lbrace -2, -1, \dotsc ,3\rbrace$  isn't true.  When you write $x \in \lbrace -2, -1, \dotsc, 3\rbrace$ you are saying "$x$ is an element of the set consisting of the integers $-2$ through $3$" which is correct.
A: If you really want to be formal you can say that the domain of $f(x)$ is $\{x \in \mathbb{Z} \mid -2 \leq x \leq 3\}$.
A: Use $\in$.  And be careful with your commas:  $\{-2, -1 \color{red}, \dots \color{red}, 3\}$
In general:
$x \in S$ means "$x$ is an element of $S$" or "$x$ is in $S$."  (The $\LaTeX$ code to produce "$\in$" is $\in$.)
$x = s$ means "$x$ is $S$" or "$x$ is equal to $S$."  In this case you would be saying $x$ is the domain, but this is not what you want to say.
