Thread: Exercise 2.1
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Old 09-19-2016, 12:03 AM
svend svend is offline
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Join Date: Sep 2016
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Default Re: Exercise 2.1

I don't understand why the breaking point inequality holds for the positive rays or positive intervals .

For instance, it seems to me that no set of 3 real points can be shattered by a positive ray, since at least always the [cross, circle, cross] dichotomy cannot be achieved, no matter how large N is, so k=3 would be a breaking point and m_H(N) < 2^3, which is obviously not true for N>7 since the real growth function is m_H(N) = N + 1.

I understand that to be a breaking point, we need that no set of size k can be shattered, am I failing to imagine such set or did I misunderstand some of the definition?
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