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On this page of Shai Shalev-Shwartz's ppt, I find it is hard for me to understand the theorem and exersise part.

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 $f$?

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