let S be a nonempty subset of R that is bounded below.prove that Inf S=-Sup {-s: s∈ S}
59872
How to prove $\inf(S)=-\sup(-S)$?
82771
Proving that any polynomial $p:\mathbb{R}\rightarrow \mathbb{R}$ is not bounded, but its restriction to any bounded set is bounded
146062
A "Cantor-Schroder-Bernstein" theorem for partially-ordered-sets
133886
Existence of increasing sequence $\{x_n\}\subset S$ with $\lim_{n\to\infty}x_n=\sup S$
93771
Prove that for any set $A$ there is some $x \notin A$
69499
Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
100565
Property of sup of a set of numbers
11834
Prove that $\liminf x_n = -\limsup (-x_n)$
76140
The supremum norm is submultiplicative
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
41477
Prove $f(S \cap T) \subseteq f(S) \cap f(T)$
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
102478
$X_n\leq Y_n$ implies $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$
152817
Proving $\sup B=\inf A$
147013
Subset of a finite set is finite
7112
Product of sets and supremum
74501
$\delta : C([0,1])\to\mathbb{R}$, $f\mapsto f(0)$, with sup-norm is bounded but unbounded with one-norm.