How to show that for $a,b\in \mathbb{C}: |a-b|=|1-a\overline{b}| \Leftrightarrow |a|=1 \, \lor \, |b|=1$
15104
Show that $\big|\frac{a-b}{1-\overline{a}b}\big|=1$, when either $|a|=1$ or $|b|=1$.
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
150738
Proof of $(A - B) - C = A - (B \cup C)$
70311
Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
18126
If $f \colon [a,b] \rightarrow \mathbb{R}$, then show that there exists $c \in [a,b]$ such that $\int_a^c f = \int_c^b f$
38200
Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
51321
Prove that $A = B = C = D$
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
31173
How to show $(a^b)^c=a^{bc}$ for arbitrary cardinal numbers?
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
144502
Showing that $A\cap B = A\setminus (A\setminus B)$
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$