For every $n$ there exists $m$ such that $m/n$ is an upper bound but $(m-1)/n$ is not
11056
Terence Tao, Analysis I, Ex. 5.5.2: Entry point needed
19823
Inequality involving $\limsup$ and $\liminf$: $ \liminf(a_{n+1}/a_n) \le \liminf((a_n)^{(1/n)}) \le \limsup((a_n)^{(1/n)}) \le \limsup(a_{n+1}/a_n)$
118353
For set of positive measure $E$, $\alpha \in (0, 1)$, there is interval $I$ such that $m(E \cap I) > \alpha \, m(I)$
148163
Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better
34929
Prove ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$.
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
96931
Supremum and infimum of $\{\frac{1}{n}-\frac{1}{m}:m, n \in \mathbb{N}\}$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
103732
Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
29084
Largest integer that can't be represented as a non-negative linear combination of $m, n = mn - m - n$? Why?
79187
Can we find $c_n$ to make $X_nc_n \rightarrow 0$ almost surely, even if $EX_n > \infty$?
31889
The limit as $n$ approaches infinity of $n(a^{1/n}-1)$
127843
Prove that, for any natural number $k$ $\exists m \in M $ s.t i) $m$ has exactly $k$ $1$'s, an
133886
Existence of increasing sequence $\{x_n\}\subset S$ with $\lim_{n\to\infty}x_n=\sup S$
118674
Simple upper bound for $\binom{n}{k}$
86518
Does $X$ have a lower bound?