Prove that $\left\{\frac{a}{2^b}: a \in\mathbb{Z}, b \in\mathbb{Z}_{\geq 0}\right\}$ is dense in $\mathbb{R}$.
98755
How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals?
113614
Approximating the density of $S\cap[a,b]$ using a Folner Sequence of $A$, where $S \subseteq A$?
157068
Prove that $\left (\frac{1}{a}+1 \right)\left (\frac{1}{b}+1 \right)\left (\frac{1}{c}+1 \right) \geq 64.$
28391
Prove the compactness of a set B
139011
How to prove $B-A \succeq 0 \Leftrightarrow$ ellipsoid $x^TBx \leq 1$ contains $x^TAx \leq 1$?
67650
Short and intuitive proof that $\left(\frac{n}{k}\right)^k \leq \binom{n}{k}$
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
135574
Help proving the primitive roots of unity are dense in the unit circle.
78915
Density of the set $S=\{m/2^n| n\in\mathbb{N}, m\in\mathbb{Z}\}$ on $\mathbb{R}$?
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
17461
Show that a set is dense in $[-1,1]$
102817
$A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
108305
How can we show that the dyadic rationals are dense in $\mathbb R$?
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
81150
Positive integer multiples of an irrational mod 1 are dense
147802
Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$