Prove that $\{e^{k\alpha \pi i}: k\in \mathbb N \}$ is dense in $S^1 $ by using(or modifying the proof of) the result when $\mathbb N$ is $\mathbb Z$
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 $S^1$
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
6523
Prove that the space has a countable dense subset
154837
mapping properties of $(1−z)^i$
12212
Showing a certain subspace of Hilbert space is dense
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
154076
How to show this property of $\mathbb{RP}^{n}$.
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
31990
Is $\{\frac{m}{10^n}\mid m,n\in\mathbb Z,\ n\geq 0\}$ dense in $\mathbb R$?
67244
Why is $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ dense in $ L^2(\mathbb{R}^n)$?
77129
Density of irrationals
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
113614
Approximating the density of $S\cap[a,b]$ using a Folner Sequence of $A$, where $S \subseteq A$?
67084
Prove or disprove that $\lim_{n \to \infty} {n \choose k} / a^n = 0$ for all $k \in \mathbb{Z_+}, a \in \mathbb{R}: a> 1$.
19858
Proving $f$ is $L^1$ implies convergence of $\sum_{k \in \mathbb{Z}}{ 2^k*m(|f| > 2^k)}$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.