Element of Group is in Unique Coset of Subgroup
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Theorem
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
Let $x \in G$.
Left Coset
There exists a exactly one left coset of $H$ containing $x$, that is: $x H$
Right Coset
There exists a exactly one right coset of $H$ containing $x$, that is: $H x$