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Let $f : [a,b] \to\Bbb R$ and $g : [a,b] \to\Bbb R$ be two continuous functions on $[a,b]$. Show that the set $\{ x \in [ a,b ] : f(x) = g(x)\}$ is closed in $\Bbb R$.

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    Here is a more general version of this question: [The set of points where two maps agree is closed?](http://math.stackexchange.com/questions/199617/the-set-of-points-where-two-maps-agree-is-closed)2012-09-20

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