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

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

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Let $f,g:\mathbb R\to \mathbb R$ which are increasing and $f(r)=g(r)$ for any $r\in\mathbb Q$. Could we must have $f(x)=g(x)$ for any $x\in\mathbb R$? Thanks in advance!

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