How to prove that $\sup \left( {{A_1} \cup {A_2}} \right) = \max \left( {\sup {A_1},\sup {A_2}} \right)$?
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
44562
If $\left|z+\frac{2}{z}\right |=2$, then prove that max value of $|z|$ is $\sqrt 3 + 1$ (Corrected version)
155999
How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
51347
Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$
43197
Showing that two definitions of $\limsup$ are equivalent
123732
Proving that the maximum of two convex functions is also convex
27482
How to show $-\sup(-A)=\inf(A)$?
24951
Suppose $f_1 \in \Theta(g_1) \land f_2 \in \Theta(g_2)$. Prove $f_1 + f_2 \in \Theta(\max\{g_1, g_2\})$.
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
16718
Doubt about step of the proof that $\limsup\limits_{n\to\infty}\left|\sum\limits_{\ell=1}^mz^n_\ell\right|^{1/n}=\max\limits_{1\le\ell\le m}|z_\ell|$
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
105768
Proof involving absolute value and maximums
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$