Does $f(\mathbb{Q}^n) \subseteq \mathbb{Q}$ hold only for rational functions?
3801
Functions that take rationals to rationals
36983
Does there exist a continuous function such that f(x) is rational for every irrational x, and f(x) is irrational for every rational x?
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
31216
Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
79281
Let $f : X \to Y$ be a function and $E \subseteq X$ and $F \subseteq X$. Show that in general
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
9966
Range of a Rational Function
151544
Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
106178
Question of an isomorphism of $\epsilon_ 0$ and a subset of the rationals.
105445
Are the rationals a closed or open set in $\mathbb{R}$?
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
75614
Proving that $n|m\implies f_n|f_m$
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$