# Can I use $x \in \{a, b, c\}$ to mean that $a, b$ and $c$ are valid solutions?

When solving an equation, can I use the notation $x \in \{a, b, c\}$ to mean that $x=a$, $x=b$ and $x=c$ are all possible solutions to the equation?

-
Well, $x \in \{a,b,c\}$ means that $x=a, x=b$ or $x=c$ but does not mention the word "solution" anywhere. –  GEdgar Oct 2 '11 at 13:40

Example: $x^3-x=0$ exactly for $x\in\{0,1,-1\}$.
By saying that $x \in \{a,b,c\}$, by definition of element of set you are saying that $x=a, x=b, x=c$ . Read more about element of set here: http://en.wikipedia.org/wiki/Element_(mathematics)