# Rationale Zahlen/Verschiedene Teilmengen/Schrankenbegriffe/Aufgabe/en

Zur Navigation springen Zur Suche springen

Examine for each of the following subsets ${\displaystyle {}M\subseteq \mathbb {Q} }$ the concepts upper bound, lower bound, supremum, infimum, maximum and minimum.

1. ${\displaystyle {}\{2,-3,-4,5,6,-1,1\}}$,
2. ${\displaystyle {}\left\{{\frac {1}{2}},{\frac {-3}{7}},{\frac {-4}{9}},{\frac {5}{9}},{\frac {6}{13}},{\frac {-1}{3}},{\frac {1}{4}}\right\}}$,
3. ${\displaystyle {}]-5,2]}$,
4. ${\displaystyle {}\left\{{\frac {1}{n}}{|}\,n\in \mathbb {N} _{+}\right\}}$,
5. ${\displaystyle {}\left\{{\frac {1}{n}}{|}\,n\in \mathbb {N} _{+}\right\}\cup \{0\}}$,
6. ${\displaystyle {}\mathbb {Q} _{-}}$,
7. ${\displaystyle {}{\left\{x\in \mathbb {Q} \mid x^{2}\leq 2\right\}}}$,
8. ${\displaystyle {}{\left\{x\in \mathbb {Q} \mid x^{2}\leq 4\right\}}}$,
9. ${\displaystyle {}{\left\{x^{2}\mid x\in \mathbb {Z} \right\}}}$.