Question about step 2(c) in the algorithm: what is the range on $\alpha_m$? Since $err_m$ is strictly positive, $\alpha_m$ ranges from $-\infty$ to $\infty$, correct? $\alpha_m = 0$ when $err_m = 0.5$.
I see $\alpha_m$ as the amount of contribution the weak classifier $G_m$ has on the final classifier, so is it possible to have negative contribution? i.e. negative $\alpha_m$?
If $err_m$ is strictly less than $0.5$, then $\alpha_m$ is strictly positive. However, how do we know that we can always find a $G_m$ with error $err_m$ that is strictly less than $0.5$?