Pumping lemma $L=\{a^ib^j | i \neq j ; i,j \ge 0\}$
118029
Pumping Lemma Excercise
47313
What is $i^i$ and $(i^i)^i$
60111
On the converse of Schur's Lemma
54380
Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
19424
Showing $(M^\perp)^\perp=\overline{M}$
95601
Is the multiplication operator on $\ell^p$ compact?
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
94077
Proof of linear independence of $e^{at}$
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
100134
Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
2626
Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$