$\{r \in \mathbb Q\mid r>0 \text{ and } r^2 < 2\}$ has no least upper bound.
4552
Choice of $q$ in Baby Rudin's Example 1.1
124456
Given $x \in \mathbb{R}$ and $N \in \mathbb{N}, N>1,$ find integers $h,k$ with $0 < k \leq N $ that satisfy $\lvert{kx - h\rvert} < 1/N.$
132595
$\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
73952
Upper bound for the sum of absolute values of the eigenvalues
131559
Lower Bound of Central Binomial Coefficients
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
102650
$\require{enclose}\enclose{horizontalstrike}{\rm Greatest}\!$ Least prime factor of $n$ is less than square root of $n$, proof
103744
Minimal $ab$ for Rational Number $a/b$ in an Interval
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
127102
Upper bound for $\sqrt[n]{n!}$
6874
smallest value of $k$ for which $a_k$ is $0$
29965
Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$
110876
Prove that $p\mid \binom{p}{k},\ 0< k< p$
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
103763
Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$