Show that for all $x\in\mathbb R$ there is a permutation $\rho : \mathbb N \rightarrow \mathbb N$ such that $\sum^{\infty}_{n=1}x_{\rho(n)}=x.$
87458
Series rearrangement and Riemann's theorem
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
96961
A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$
105952
If each $a_n >0$ and $\sum a_n$ diverges, prove that $\sum a_n x^n \to +\infty$ as $x\to1^-$.
153612
Finding $g_i:\mathbb{R}^n\to\mathbb R$ s.t $f(x)=\sum\limits_{i=1}^nx_i\cdot g_i(x)$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
15909
Bijection from $\mathbb R$ to $\mathbb {R^N}$
14986
Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$
77973
How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.
97878
Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
72551
Proof that $\rho = \pm1$ implies linear combination
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
125876
Sum and Product of Infinite Radicals
128966
Explicit bijection between $\Bbb R$ and permutations of $\Bbb N$