Let $x$ be an irrational number. Is the set $\ \{nx \mod 1: n \in \mathbb{N} \}\ $ dense in $[0,1]\ ?$
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
73336
If $A$ is a nowhere dense subset of a topological space $X$, then $X\setminus A$ is dense in $X$.
85870
Show this set is a base for some topology on $\mathbb{Z}$
19676
Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?
140300
Does the interval $[0,1]$ contains more real numbers than $(0,2)$?
31990
Is $\{\frac{m}{10^n}\mid m,n\in\mathbb Z,\ n\geq 0\}$ dense in $\mathbb R$?
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
138446
Proving that there exists an irrational number in between any given real numbers
30478
How to prove that a number is irrational
18360
Proof that the irrational numbers are uncountable
27889
If the set of odd numbers is a subset of $\mathbb N$ then surely it is smaller than $\mathbb N$
79144
Prove that the orbit of an iterated rotation of 0 (by (A)(Pi), A irrational) around a circle centered at the origin is dense in the circle.
74498
Smallest dense subset of $\mathbb{R}$
32
Is $n^{th}$ root of $2$ an irrational number?
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
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 $S^1$
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?