Regularity method: size of $\epsilon$-regular graph parts

Question

I am applying the Regularity method, as described for example here.

I do not understand why the size $l$ of the $k$ resulting sets $V_i$, ie:

$l = |V_1| = |V_2| = ... = |V_k|$

has the following size, after the sets has been made super-regular:

$$\frac{n(1 - \epsilon)}{M(\epsilon)} \le l$$

With $M(\epsilon)$ being the upper bound on $k$.

I understand the $n/M(\epsilon)$ part: each set can have at most $n$ elements divided by the $M(\epsilon)$, the maximum number of parts. But where is the $(1 - \epsilon)$ term coming from?

Answer 1

The $1−ϵ$ term is coming from the $V_0$ part of size at most $ϵn$, thanks Erick!