graph theory - Szemeredi's Regularity Lemma

Theorem: (SRL)
For every $epsilon>0$ and integer $mgeq 1$ there is an $M$ such that every graph $G$, with $|G|geq m$ has an $epsilon$-regular partition $V(G)=V_0cupldotscup V_k$ for some $mleq kleq M$.

Can someone explain to me why this statement is not trivial? For instance, what stops me choosing $M$ larger than $|G|$ and picking $k=|G|$, so I can split $G$ up into singletons, which is trivally $epsilon$-regular for any $epsilon>0$.