Partition einer Menge

Als Partition einer Menge bezeichnet man die Zerlegung einer Menge in Teilmengen , sodass jedes Element der Menge in genau einer dieser Teilmengen enthalten ist.

Beispiel

Gegeben ist die Menge $\mathrm{A}=\{\mathrm{1,2},3\}\backslash mathrm\; A=\backslash left\backslash \{1\{,\}2,3\backslash right\backslash \}$.

Mögliche Partitionen dieser Menge sind:

${\mathrm{P}}_1=\{\left\{1\right\},\left\{\mathrm{2,3}\right\}\}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{r}{\mathrm{P}}_2=\left\{\{\mathrm{1,2},3\}\right\}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{r}{\mathrm{P}}_3=\{\left\{1\right\},\left\{2\right\},\left\{3\right\}\}\{\backslash mathrm\; P\}\_1=\backslash left\backslash \{\backslash left\backslash \{1\backslash right\backslash \},\backslash left\backslash \{2\{,\}3\backslash right\backslash \}\backslash right\backslash \}\backslash ;\backslash mathrm\{oder\}\backslash ;\{\backslash mathrm\; P\}\_2=\backslash left\backslash \{\backslash left\backslash \{1\{,\}2,3\backslash right\backslash \}\backslash right\backslash \}\backslash ;\backslash mathrm\{oder\}\backslash ;\{\backslash mathrm\; P\}\_3=\backslash left\backslash \{\backslash left\backslash \{1\backslash right\backslash \},\backslash left\backslash \{2\backslash right\backslash \},\backslash left\backslash \{3\backslash right\backslash \}\backslash right\backslash \}$.

Dagegen ist $Q=\{\left\{\mathrm{1,2}\right\},\left\{\mathrm{2,3}\right\}\}Q=\backslash left\backslash \{\backslash left\backslash \{1\{,\}2\backslash right\backslash \},\backslash left\backslash \{2\{,\}3\backslash right\backslash \}\backslash right\backslash \}$ keine Partition von $\text{A=}\{\mathrm{1,2},3\}\backslash text\{A=\}\backslash left\backslash \{1\{,\}2,3\backslash right\backslash \}$.