Regarding Errors; In the intro formula: p(z_i = k |z_{1,\dots,i-1},\alpha,K) = \frac{n_k + \frac{\alpha}{K}}{i-1+\alpha} seems flawed. Shouldn't i be replaced with something like N = \sum_{k=1}^{K} n_k and in all formulas below pertaining to the derivation of DP as the limit of the of a DM distribution?