I need some help to understand the proof of this theorem below. I tried several times to understand the proof, but I failed.
Specifically, I do not understand how and why you get $\mathbf{K} = \mathbf{K}(\frac{\epsilon}{\mathbf{C}})$
Until now I was familiar with getting K to be something like $\mathbf{K} > \frac{\epsilon}{\mathbf{C}}$ and then proceed to proof the limit of a sequence. However, in the proof below, equality is used instead of inequality and $\mathbf{K}$ is assigned with itself with some constant $\frac{\epsilon}{\mathbf{C}}$.
