Let $S\subset\mathbb R$ be a non-empty bounded set and let $T$ be a non-empty subset of $S$.
Is $T$ bounded from below and does $\inf(S)\le \inf(T)$ hold?
And if $S$ satisfies $\sup(S)=\inf(S)$ imply, does that mean $S$ is a singleton set?
Let $S\subset\mathbb R$ be a non-empty bounded set and let $T$ be a non-empty subset of $S$.
Is $T$ bounded from below and does $\inf(S)\le \inf(T)$ hold?
And if $S$ satisfies $\sup(S)=\inf(S)$ imply, does that mean $S$ is a singleton set?