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?
Can I use $x \in \{a, b, c\}$ to mean that $a, b$ and $c$ are valid solutions?
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elementary-set-theory
notation
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0Well, $x \in \{a,b,c\}$ means that $x=a, x=b$ or $x=c$ but does not mention the word "solution" anywhere. – 2011-10-02
2 Answers
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It is indeed an acceptable notation.
Example: $x^3-x=0$ exactly for $x\in\{0,1,-1\}$.
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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)