Use of domain notation

Question

Is it incorrect to write $s \neq \left\{2,-2\right\}$?

If yes, is the proper notation $s \notin \left\{2,-2\right\}$?

Answer 1

The two are different:

the first one is to be read: the set $s$ is not equal to the set $\{2,-2\}$.

the second one is indeed the classical $s\neq 2\land s\neq-2$

Answer 2

Writing $s \neq \{-2,2\}$ means that the set $s$ is not the two element set $\{-2,2\}$. Writing $s \notin \{-2,2\}$ means that $s$ is not the number $-2$ or $2$.

Answer 3

With the first notation you compare to sets. In this you say that set s is not equal to the unnamed set $\{2, -2\}$. With the second notation you express that the set s doesn't contain the elements 2 and -2. If you want to express the domain of a function then you could express it in this way: D = $\{ x \in \mathbb{R} | x \notin \{2, -2\}\}$