I need a continuous function $f:\mathbb{Q}\rightarrow \mathbb{R}$ and discontinuous $g:\mathbb{R}\rightarrow \mathbb{R}$ s.t $f(x)=g(x)$ for all rational $x$ s. So if I say $f(x)=0$ and $g(x)=0$ for $x \in \mathbb{R}\setminus\{\sqrt2\}$ and $g(x)=1$ at $x=\sqrt 2$ .would I be right?
Continuity On $\mathbb{Q}$
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real-analysis
general-topology
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0yes,you are right – 2012-11-03