The course is amazing! (And the proof has been given in the comment by Pete :) )
I'm so sorry for my delay -- after several travels within the last months and new/old papers, I fell behind but I'm trying to catch up. I'm so happy to go through the course material and reading the lectures, very thought-provoking. There is a depth of thinking that goes way beyond a beginning course stuff, and I've the feeling that I should learn this thinking style too.
It's a bit out of topic, but I hope you can enjoy a rhythm I derived from the numerical sequence on the 'Just For Fun 1.' Many new ideas arise! :) Thank you for all of this!