How to show that $\{\sqrt m - \sqrt n : m,n \in \mathbb N\}$ is dense in $\mathbb R$?
90590
Prove that the following set is dense
150337
Let $K$ be a subfield of $\mathbb{C}$ not contained in $\mathbb{R}$. Show that $K$ is dense in $\mathbb{C}$.
106434
Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
30568
Let $q \in \mathbb C$, $\|q\|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n: n \in \mathbb N\}$ is dense in $S^1$
44496
Norm $N$ on $\Bbb Z[\sqrt d]$ is multiplicative, $N(x)$ prime $\Rightarrow x$ irreducible
154076
How to show this property of $\mathbb{RP}^{n}$.
33309
Subgroup of $\mathbb{R}$ either dense or has a least positive element?
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
81150
Positive integer multiples of an irrational mod 1 are dense
113614
Approximating the density of $S\cap[a,b]$ using a Folner Sequence of $A$, where $S \subseteq A$?
86807
The units of $\mathbb Z[\sqrt{2}]$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
35691
$\mathbb Z[\sqrt 3]$ contains infinitely many units
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$