query: Does exist a continuous real valued function on the rational number but discontinuous on the irracional numbers?
positive_passages.docid: 18222
positive_passages.text: Set of continuity points of a real function
negative_passages.docid: 60700
negative_passages.text: Continuity of a function to the integers
negative_passages.docid: 40070
negative_passages.text: Is there a real-valued function $f$ such that $f(f(x)) = -x$?
negative_passages.docid: 137883
negative_passages.text: Cardinality of the set of all (real) discontinuous functions
negative_passages.docid: 76607
negative_passages.text: Show that exists a continuous function in $E$ that is not bounded
negative_passages.docid: 88240
negative_passages.text: Two functions discontinuous, but sum continuous
negative_passages.docid: 120947
negative_passages.text: continuous real-valued function
negative_passages.docid: 29180
negative_passages.text: If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
negative_passages.docid: 32571
negative_passages.text: Is the maximum function of a continuous function continuous?
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: 124444
negative_passages.text: If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
negative_passages.docid: 61500
negative_passages.text: If f is continous and exist real numbers show that $f(x)=0$
negative_passages.docid: 154572
negative_passages.text: Continuity of a function at an isolated point
negative_passages.docid: 83446
negative_passages.text: bijective continuous function on $\mathbb R^n$ not homeomorphism?
negative_passages.docid: 87131
negative_passages.text: Discontinuous at rationals and differentiable at irrationals?
negative_passages.docid: 73594
negative_passages.text: Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$
negative_passages.docid: 128911
negative_passages.text: Continuous extension of a real function