query: Is there any function continuous only at rationals?
positive_passages.docid: 158309
positive_passages.text: Find a function that is continuous only on rationals
negative_passages.docid: 69869
negative_passages.text: if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
negative_passages.docid: 83204
negative_passages.text: Is every $G_\delta$ set the set of continuity points of some function $f$?
negative_passages.docid: 41841
negative_passages.text: Function with limits only at irrational points
negative_passages.docid: 128911
negative_passages.text: Continuous extension of a real function
negative_passages.docid: 101230
negative_passages.text: Example of an increasing, integrable function $f:[0,1]\to\mathbb{R}$ which is discontinuous at all rationals?
negative_passages.docid: 102075
negative_passages.text: A function continuous on all irrational points
negative_passages.docid: 18222
negative_passages.text: Set of continuity points of a real function
negative_passages.docid: 30590
negative_passages.text: Are "most" continuous functions also differentiable?
negative_passages.docid: 25010
negative_passages.text: Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$
negative_passages.docid: 60700
negative_passages.text: Continuity of a function to the integers
negative_passages.docid: 87131
negative_passages.text: Discontinuous at rationals and differentiable at irrationals?
negative_passages.docid: 97619
negative_passages.text: Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
negative_passages.docid: 62817
negative_passages.text: Functions which are Continuous, but not Bicontinuous
negative_passages.docid: 3801
negative_passages.text: Functions that take rationals to rationals
negative_passages.docid: 130019
negative_passages.text: Function that is continuous only on the transcendental numbers
negative_passages.docid: 41201
negative_passages.text: How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.