Proving $ \sup (E_1 \cup E_2) = \max \{ \sup E_1, \sup E_2 \}$
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
33030
Proof that $\inf A = -\sup(-A)$
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
22224
Define $S\equiv\{ x\in \mathbb{Q}\mid x^2<2\}$. Show that $\sup S=\sqrt{2} $.
8617
How do you prove ${n \choose k}$ is maximum when $k$ is $ \lceil \tfrac n2 \rceil$ or $ \lfloor \tfrac n2\rfloor $?
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
87536
Supremum of the infimum
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| $
10107
Prove $A\cup (A\cap B) = A$
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
95513
Proving $W$ is a subspace of $P_{2}$
143900
how can be prove that $\max(f(n),g(n)) = \Theta(f(n)+g(n))$
145058
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
107894
Inequality involving the sup of a function and its first and second derivatives
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$