Is there any positive function $f$ such that $f(x)f(y)\leq |x-y|$ for every $x$ rational and $y$ irrational?
6636
Is there a positive function $f$ on real line such that $f(x)f(y)\le|x-y|, \forall x\in \mathbb Q , \forall y \in \mathbb R \setminus \mathbb Q$?
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
133496
is $\sqrt{x}$ always positive?
849
$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
118348
Let $x$ be transcendental over $F$. Let $y=f(x)/g(x)$ be a rational function. Prove $[F(x):F(y)]=\max(\deg f,\deg g)$
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
127887
Existence of a meromorphic functions $f(z)$ such that $|f(z)|\geq |z|$.
99820
symetric inequality for a rational function of three variables
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
64905
Let $f \in C [a,b]$ such that $\forall x\exists y$ such that $|f(y)| \leq \frac{1}{2}|f(x)|$. Prove that $\exists c\in [a,b]$ such that $f(c) = 0$.
132478
Prove that continuous functions mapping irrationals to rationals must be constant
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
95787
Prove or find a counterexample: For all real numbers x and y it holds that x + y is irrational if, and only if, both x and y are irrational.
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
107518
Entire function $f$ such that $|f(z)| ≤ K |z|^3$ for $|z|\ge1$ and $f(z) = f(iz)$ for every $z∈C$