Two monotone functions which equal on rational numbers – math.stackexchange.com

Two monotone functions which equal on rational numbers – math.stackexchange.com

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Let $f,g:\mathbb R\to \mathbb R$ be increasing and $f(r)=g(r)$ for every $r\in\mathbb Q$. Must we have $f(x)=g(x)$ for every $x\in\mathbb R$? Thanks in advance!

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