I'm reading the book Complex Analysis by Bak and Newman.
I understand everything in the proof below - except for the constant 2 in the bound. Can someone explain me where the factor of 2 comes?
Few notational clarifications: For complex $a$ and $b$, $a << b$ means $|a| \leq |b|$
ML theorem refers to a theorem that says that a curve integral can be bound by the maximum value $M$ and the length $L$.
I've tried to point the step that confuses me with a red circle. I don't know where the factor of 2 comes in that bound. Length is $h$ and the integral should be bounded by $\epsilon$, thus $h \epsilon$ ? So where does $2h \epsilon$ come from? Both bounds are okay for the proof but I'm just curious if I'm missing something.
