1. Sets

infimum: greatest lower bound. Written $\sup (x)$ supremum: least upper bound. Written $\inf (x)$

• Infimum and supremum always exist if well-ordered. $\sup (x)=\infty$ and $\inf (x)=\infty$ possible.
• If a set is half-open, like $[3,5)$, then it doesn’t have a maximum because for every number 4.999…, there is another number with even more digits. However, it does have a supremum.
• If a set has a minimum, it has an equivalent infimum. Analogous for maximum and supremum.

compact Interval: abgeschlossen und beschränkt