proof of $2^{\aleph_0} = \mathfrak c$
41052
The set of real numbers and power set of the natural numbers
43598
Do $\omega^\omega=2^{\aleph_0}=\aleph_1$?
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
65141
Simple proof Euler–Mascheroni $\gamma$ constant
75625
Complete residue system proof
102398
Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
55621
Show that if $c_1, c_2, \ldots, c_{\phi(m)}$ is a reduced residue system modulo m, $m \neq 2$ then $c_1 + \cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
137369
Inductive proof of gcd Bezout identity (from Apostol: Math, Analysis 2ed)
26497
Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
23557
Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
25967
Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$
100134
Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
4782
Can we distinguish $\aleph_0$ from $\aleph_1$ in Nature?