Science:Math Exam Resources/Courses/MATH220/December 2009/Question 09 (a)/Statement

Find the supremum, maximum, infimum, and minimum of the following subsets of $\mathbb {R}$ (if they exist). If they do not exist write "none". You do not need to justify your answers.

set	supremum	maximum	infimum	minimum
$\{x\in \mathbb {R} \quad {\textrm {s.t.}}\quad {}7<x\leq 10\}$
$\{x\in \mathbb {Q} \quad {\textrm {s.t.}}\quad {}x^{2}<3\}$
$\{x\in \mathbb {Z} \quad {\textrm {s.t.}}\quad {}x^{2}<3\}$
$\bigcap _{n=1}^{\infty }\left(1-{\frac {1}{n}},4+{\frac {1}{\sqrt {n}}}\right)$