How to prove $\inf B = -\sup A$
33030
Proof that $\inf A = -\sup(-A)$
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
129480
Prove that inf(A+B) = infA + infB
29849
How can I show that $\sup(AB)\geq\sup A\sup B$ for $A,B\subset\mathbb{R}$ where $A\cup B$ is positive and bounded?
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
147941
comparing sup and inf of two sets
144502
Showing that $A\cap B = A\setminus (A\setminus B)$
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
50266
In the following figure prove that: $AK||BC$
40524
Let $A \subseteq (0,\infty$) such that $\inf A>0$. Let $\frac{1}{A}=\{\frac{1}{a},a\in A\}$. Prove that $\sup \frac{1}{A}=\frac{1}{\inf A}$.
158695
Prove that if $AB$ is invertible then $B$ is invertible.
125030
Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
155999
How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
143130
Proving that the supremum of $(a,b)$ is $b$.