In the theorem part, I know that the first part is always true, since if a sample $$x$$ in the data set is labled with 1, we can use this $$x-\epsilon$$ as the $$\theta$$, and the trivial condition is that the sequence only have one example, that is $$x$$. But I can't understand and prove the later part. I mean, what is the meaning of "always?"
In the exercise part, I can't see why we can't learn the class of axis-aligned rectangles. Additionally, does the exercise here means that the function $$f$$ we learned should be the real predicator? That is,all points in $$\mathbb{R}$$ should be consistent with $$f$$?