prove that $\mathbb{Q}$ can not be $G_{\delta}$ set in $\mathbb{R}$.
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
140430
Let $E = \mathbb{Q}\big(\left\{\sqrt[n]{2} \mid n \in \mathbb{N} \setminus \left\{0\right\} \right\} \big)$. Prove $[E: \mathbb{Q}]$ is not finite
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
5035
Can unprovability unprovable? Is there an $\omega$-fold unprovability?
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
107370
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
130073
$N(ab) \geq N(a)$ is not necessary for the ring to be euclidean
100919
Examples of non-measurable sets in $\mathbb{R}$
149820
How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed?