Prove that the set $S$ of rational points in the plane $\mathbb R^2$ is denumerable.
38507
Show that $\mathbb{Q}\times \mathbb{Q}$ is denumerable
12701
Perfect set without rationals
156479
Fractal dimension of set in $\mathbb{R}^2$
134726
Show the polynomial is irreducible in $\textbf Z_2$
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
158155
Is set of isolated points of S closed?
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
114262
Find the cardinality of the following set $S_n=\{(x,y)|x^2+y^2=n, \text{where }x,y,n \in \mathbb Z\text{ and }n\geq0 \}$
4518
How would one go about proving that the rationals are not the countable intersection of open sets?
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
23851
Is there a set of lines in $\mathbb{R}^3$ such that their union is equal to the set of points with not all coordinates rational?
40162
Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$