1. ## Supremum and Infima

Hi all,

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

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

Nice nickname, Euler.