We have the following equivalence relation:
$$x\,p\,y\iff x-y\in\Bbb C$$
Find a Complete and Independent System of Representatives (CISR). Let $S$ be the CISR.
What I know: $S\subseteq\Bbb C$ and $S$ is:
- Complete: $\forall x \in\Bbb C, x\,p\, X$ for some $X \in S$. (Every element of $\Bbb C$ has a class representative)
- Independent: $Y\, \lnot p\, Z$ if $Y,Z \in S$. (There are no equivalent classes in $S$)
How should I find $S$?