Proving $\sup X=-\inf(-X)$
27482
How to show $-\sup(-A)=\inf(A)$?
81203
Supremum and infimum of sets
17542
Why is $\sqrt{-x}*\sqrt{-x}=-x?$
141837
Proof of $\sup\{ (n!)^{(\frac{1}{n})}| n ∈ N\} = +∞?$
105107
How to explain the following definition of $\lim\sup s_n$ intuitively?
125011
Show lim sup (an) = lim inf (an) for increasing for increasing sequence of subsets.
24856
Proving sup(A + B) = sup A + sup B
87848
Formal proof for $(-1) \times (-1) = 1$
22224
Define $S\equiv\{ x\in \mathbb{Q}\mid x^2<2\}$. Show that $\sup S=\sqrt{2} $.
153272
Basic question about $\sup_{x\neq 0}{} \frac{\|Ax\|}{\|x\|} = \sup_{\|x\| = 1}{\|Ax\|} $, $x \in\mathbb{R}^n$
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
11834
Prove that $\liminf x_n = -\limsup (-x_n)$
107765
Prove that there exists two roots in $[-1,1]$
28822
$|x| - |y| \leq |x-y|?$
126632
Proving Inequalities with Absolute values
10859
Prove $\sup(f+g) \le \sup f + \sup g$