For example, when he discusses power sets in order to introduce sigma algebras, he implies that a sigma algebra is a better-behaved alternative to a power set. However, a power set is always itself a sigma algebra (after all, even a power set of an uncountable set still is closed under complements and countable unions).
Later, when discussing probability distributions, he writes:
> [W]e want this allocation [of a conserved quantity] to be self-consistent – the allocation to any collection of disjoint sets, A_n ∩ A_m=0, n≠m, should be the same as the allocation to the union of those sets, > ℙπ[∪(n=1 to N) A_n]=∑(n=1 to N)ℙπ[A_n].
The condition `A_n ∩ A_m=0, n≠m` is actually incorrect, since A_n and A_m are sets and 0 is an integer. The author means the empty set, but typo'd.
Sometimes he frequently uses words like "conserved" or "well-defined" without giving us a clue as to what these mean. In what context are probabilities "conserved"? What distinguishes "well-defined" from "not well-defined"?
I'm a software engineer. A non-trivial amount of my time is devoted to reading code and finding bugs. Sloppy reasoning, inconsistencies and outright errors like that are big red flags to me. It doesn't help that the whole section on sigma algebras is somewhat irrelevant, since he doesn't really explore measure theory as the basis for modern probability.
IMO a better resource is the series of "Probability Primer" videos from mathematicalmonk on YouTube[1]. He does an excellent job (IMO) of covering all pertinent pre-requisites and being mostly rigorous without necessarily proving every single fact or exhaustively covering all edge and corner cases. He also makes a good effort to recommend advanced (and rigorous) treatments of the subject (and ancillary ones like measure theory). A readable version of this YouTube series would be a great resource, and if Michael Betancourt is reading, I'd encourage him to pursue that in his next iteration of this product.