Help with this proof about sup and inf
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
155999
How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
132595
$\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
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| $
133884
A proof using Yoneda lemma
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
31522
Proving $f$ has at least one zero inside unit disk
87536
Supremum of the infimum
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
96848
Prove: $\limsup_{n\to\infty} (a_n)\leq \sup(a_n)_{n=1}^\infty$
148500
Understanding this theorem and how to go about proving it surjectivity?
122832
Proof for SSS Congruence?
27482
How to show $-\sup(-A)=\inf(A)$?
69184
Proof that absolute value of supremum equals suprememum of absolute value
106799
Proof Verification: Converse of Intermediate Value Theorem
143130
Proving that the supremum of $(a,b)$ is $b$.
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$