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$$S = \{(x_1, x_2, x_3) \in \mathbb{R}^3\ |\ x_2 − (x_1)^2 = 0\}$$

I found this question in an old exam and I'm not sure how to prove this question, but I know it is not a subspace. Any help is appreciated.

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    Find two things in it. Unless you are very unlucky, their sum won't be in it. Or, find one thing in it. Unless you are very unlucky, the negative of that thing won't be in it.2012-09-21
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    A question is not a statement; to "prove a question" makes no sense.2012-09-21
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    @GerryMyerson: The quickest thing to find is $(0,0,0)$, which is going to make him rather unlucky either way.2012-09-21

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