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Can we draw this function? $f\colon\mathbb{R}\to\mathbb{R}$, given by $f(x) = \left\{\begin{array}{ll} 1 &\mbox{if $x\in\mathbb{Q}$;}\\ 0 &\mbox{if $x\notin\mathbb{Q}$.} \end{array}\right.$

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    @Mopz$e$r: There *isn't* that much information asbout this function: it takes exactly two values, both of them on dense sets; it is discontinuous everywhere, but that is not something draw a "drawing" will let you see. There are **physical limits** to what you can represent pictorially, and an accurate representation of this function is well beyond those limits.2011-04-16

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It depends upon what you mean by "draw". You could draw a dotted line along $y=0$ and another along $y=1$ with the dots meaning that the function is not continuous and so some of the points you (seem to) have covered are not part of the function. If by draw you mean a continuous curve in the plane, no you cannot, because the function is not continuous.

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    Ok makes sense ${}$2018-07-19