The whole point of the article is that we don't know which infinity it is.

I didn't read the paper, and have only an undergraduate math background, but it seems to me that for sufficiently large n, n + 1 = n. Vague justifications related to limits.

They know it is infinite. They want to understand the cardinality. Any two sets (including infinite sets) A, B have the same cardinality if there exists a bijection from A|->B