Could someone explain the the conclusion of this proof that the Julia set is bounded to me?
Theorem: The Julia set of a function is compact for all
Proof: First, we show that is bounded.
Choose and let .
Then we have,
And so we have,
Hence, since then
(*)
And so . (**)
I found this in a journal, I don't really understand how the last line (**) happens. Surley (*) shows the function diverges... How can we say it's bounded?