First, a general comment: Prof. Abu-Mostafa made things really really clear, my million thanks!

Here I have a small confusion: On p.55, line 6, it says "(What the growth function ...), so we can get a factor similar to the '100' in the above example".

The analogy makes the general idea 100 times more comprehensible than plunging into the proof directly. However, here I minded a gap. Can anybody help if this is my misunderstanding or I am right in this point

?

- the '100' is a "good" guy in the above example, which "condenses" (so shrink) the coloured area that times much.

- the growth function, on the other hand, is a bad guy, which gives that much ways for hypotheses behaving differently on the canvas, and "smears" the colours

So I think they are more inversely comparable, e.g. if the example is given as follows:

However many hypotheses in

, then can only behave in

ways. Therefore, each point on the canvas that is coloured will be coloured

times.