query: Question about the existence of a specific function $f: \mathbb{R} \to \mathbb{R}$
positive_passages.docid: 47992
positive_passages.text: Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
negative_passages.docid: 80210
negative_passages.text: It is posible to have a function $f$ with the following property?
negative_passages.docid: 23186
negative_passages.text: $f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$
negative_passages.docid: 148328
negative_passages.text: Example of a function $f$ on $X$ to $\mathbb{R}$ which is not $X$-measurable but $|f|$, and $f^2$ are measurable.
negative_passages.docid: 102143
negative_passages.text: $f:\mathbb R\rightarrow \mathbb R$ be a continuous function such that $\int_{0}^{\infty}f(x)dx$ exists.
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 40070
negative_passages.text: Is there a real-valued function $f$ such that $f(f(x)) = -x$?
negative_passages.docid: 18334
negative_passages.text: Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
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: 62568
negative_passages.text: Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
negative_passages.docid: 62723
negative_passages.text: If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere
negative_passages.docid: 42218
negative_passages.text: How to find out the following function f which is a function of r?
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 144426
negative_passages.text: Example of a function $f:\mathbb{R}^2\to\mathbb{R}$ not differentiable at $(0,0)$, but has a directional derivative at $(0,0)$ in all directions
negative_passages.docid: 143354
negative_passages.text: Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
negative_passages.docid: 17154
negative_passages.text: Does a non-trivial solution exist for $f'(x)=f(f(x))$?
negative_passages.docid: 62744
negative_passages.text: Does the functional equation $f(1/r) = rf(r)$ have any nontrivial solutions besides $f(r) = 1/\sqrt{r}$?