How to show that that Dyadic rational are dense in R.
108305
How can we show that the dyadic rationals are dense in $\mathbb R$?
129205
A question about uncountable, dense sets in R
106434
Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
105445
Are the rationals a closed or open set in $\mathbb{R}$?
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
78915
Density of the set $S=\{m/2^n| n\in\mathbb{N}, m\in\mathbb{Z}\}$ on $\mathbb{R}$?
51514
Is $n \sin n$ dense on the real line?
22865
Sine function dense in $[-1,1]$
145726
For a subfield $K$ of $\Bbb C$ with $K\nsubseteq \Bbb R$, show $K$ is dense in $\Bbb C$.
13550
For an irrational number $\alpha$, prove that the set $\{a+b\alpha: a,b\in \mathbb{Z}\}$ is dense in $\mathbb R$
54496
Showing that $\mathbb{R}$ and $\mathbb{R}\backslash\mathbb{Q}$ are equinumerous using Cantor-Bernstein
47730
graph is dense in $\mathbb{R}^2$
26256
Characterizing Dense Subgroups of the Reals
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
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 $S^1$
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
132382
Showing a set is nowhere dense in $C([0,1])$