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I was asked in a exam: does there exist a function(need not be continous) $f:\mathbb{R}\rightarrow \mathbb{R}$ whose graph is dense in $\mathbb{R}^2$?

I proved that graph of a discontinuous linear map is dense but did not provide explicit example, could any one give me one such? thank you

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    See [Function with range equal to whole reals on every open set](http://mathoverflow.net/questions/32126/function-with-range-equal-to-whole-reals-on-every-open-set/) at MO Many examples from this question have the same property: [Can we construct a function $f:\mathbb R\to \mathbb R$ such that it has intermediate value property and discontinuous everywhere?](http://math.stackexchange.com/questions/21812/)2012-11-02

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