Prove $o(u^{-1})=o(u)$ for all $u \in G$ and $o(uh)=o(hu)$ for all $u,h \in G$.
34973
Is it true that the order of $ab$ is always equal to the order of $ba$?
44328
Prove that $\sum_{k=1} ^ n k^{-1} = \ln(n) + O(1)$
49296
Prove $|(1+|u|^2)v-(1+|v|^2)u|>|u\bar{v}-\bar{u}v|$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
54380
Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$
15089
Big-O: If $f(n)=O(g(n))$, prove $2^{f(n)}=O(2^{(g(n)})$
34702
Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
10859
Prove $\sup(f+g) \le \sup f + \sup g$
146760
Prove that H is a subgroup of G
150738
Proof of $(A - B) - C = A - (B \cup C)$
76610
Show that $f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
82935
Prove that f∈Θ(g)if and only ifO(f) =O(g).
99821
Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$.