Currently a high school sophomore, my math curriculum doesn't go into the formal foundations of the math we learn and I'm looking to clarify a very specific idea.
(assuming we are dealing with one equation with one unknown variable): We began in algebra by learning to solve simple linear equations where the variable, let's say $x$ is equal to some number $a$, i.e. $x=a$. Then came polynomials where your variable can equal more than one number, i.e. $x=\{a_1,a_2,...a_n\}$.
This is where the problem arises. x is a $number$, not a set, so wouldn't it really make sense to say about the solution to an algebraic equation that $x\in\{a_1,a_2,...a_n\}$?
This answer is accredited to @mweiss
Yes, it would make more sense to say that. But it is common to misuse notation, especially where it is clear what is meant.