# Math Help - Supremum and Infima

1. ## Supremum and Infima

Hi all,

Given a set:
$x \in (-\infty, -2] \cup [-1, \infty)$
would you say that, the least upper bound and greatest lower bound do not exist.
and subsequently for:
$x \in (\frac{-\sqrt{29}}{2}+\frac{3}{2}, \frac{\sqrt{29}}{2}+\frac{3}{2})$, That the least upper bound is $(\frac{\sqrt{29}}{2}+\frac{3}{2})$ and the lower bound is $(\frac{-\sqrt{29}}{2}+\frac{3}{2})$

2. Originally Posted by Oiler
Given a set:
$x \in (-\infty, -2] \cup [-1, \infty)$
would you say that, the least upper bound and greatest lower bound do not exist.
and subsequently for:
$x \in (\frac{-\sqrt{29}}{2}+\frac{3}{2}, \frac{\sqrt{29}}{2}+\frac{3}{2})$, That the least upper bound is $(\frac{\sqrt{29}}{2}+\frac{3}{2})$ and the greatest lower bound is $(\frac{-\sqrt{29}}{2}+\frac{3}{2})$
Yes to both questions. When you specify a set, write just $(-\infty, -2] \cup [-1, \infty)$, not $x \in (-\infty, -2] \cup [-1, \infty)$.

Nice nickname, Euler.