## Induced magma power set magma

### Set

 context $\langle\!\langle M,* \rangle\!\rangle$ … magma definiendum $\langle\!\langle {\mathcal P}M,\star \rangle\!\rangle$ definition $\star\in$ binary operation on ${\mathcal P}M$ definition $S\star T:=\{x*y\ |\ x\in S, y\in T\}$

#### Discussion

When talking about left cosets etc., people write $xS$ for $\{x\}S$.

Wikipedia: Magma