Boosting algorithms: Confusion between "weak classifiers" versus "number of boosting rounds" I've been reading up on boosting algorithms.

I understand that the main crux of the algorithm is to build weak classifiers that are slightly better than random guessing, and then to add them up so that we end up with a strong classifier. This is done via "boosting rounds".

With different papers using different variables, like k, n, m, etc, it's gotten a bit confusing.

I just want to confirm, if I run a boosting algorithm for, say 150 rounds, is that equivalent to saying that I'm training 150 weak classifiers? I mean, is a weak classifier the output of one boosting round?
I went back to the original paper from the literature by Schapire (http://www.cs.utah.edu/~piyush/teaching/brief_intro_boosting.pdf) and it does sound like a weak classifier is the output of a boosting round. Consider how the output of the overall classifier is $$H(x)= \text{sign}\left(\sum_{t=1}^T\alpha_th_t(x)\right)$$ which is expressing a threshold for the sum of $T$ weak classifiers.