Description on page 55

[junjy]

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.

[yaser]

Originally Posted by junjy

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.

You are correct in the characterization of good and bad guys. The redundancy accounting through factors like 100 is just a technical way to get a handle on the growth function, so indeed they work in opposite directions.

[junjy]

Thank you for the clearance!