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
is, so
would be a breaking point and
, which is obviously not true for
since the real growth function is
.
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?