Formal distinction between $x=a$, where a is a number, vs $x=\{a_1, a_2, ..., a_n\}$ where x is a solution to an algebraic equation

Question

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 $x\in\{a_1,a_2,...a_n\}$?

Yes, it would make more sense to say that. But it is common to misuse notation, especially where it is clear what is meant. — mweiss, Mar 29 '16 at 01:30
Yeah thanks. The thing is you master the rules before you break them so my perception of the rigor of mathematics left the fact that notation can be misused out of my hypothesis space. — theideasmith, Mar 29 '16 at 01:33

score 0 · Answer 1 · answered Mar 29 '16 at 01:32

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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.

answered Mar 29 '16 at 01:32

theideasmith

1,090

As a general tip on StackExchange, when you want to post an answer that came out of the comments and is multiple people's ideas, you should post it under "community wiki" so that everyone can edit it and not one person gets reputation or credit for the answer. – Noble Mushtak Mar 29 '16 at 01:35
You have already made the change. This is now a community wiki post. – Noble Mushtak Mar 29 '16 at 01:43

Formal distinction between $x=a$, where a is a number, vs $x=\{a_1, a_2, ..., a_n\}$ where x is a solution to an algebraic equation

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