[samoright]

Can you simplify for us what exactly have the mathematicians in this article proven?

I get that they have proven some infinity A = some infinity B but can you tell us what these A and B are.

Also, isn't the cardinality of reals equinumerous with that of the cardinality of the power set of naturals?

[ColinWright]

Quoting from the article:

> Briefly, p is the minimum size of a collection of infinite sets of the natural numbers that have a “strong finite intersection property” and no “pseudointersection,” which means the subsets overlap each other in a particular way; t is called the “tower number” and is the minimum size of a collection of subsets of the natural numbers that is ordered in a way called “reverse almost inclusion” and has no pseudointersection.

In short, there are two infinities, p and t, that are implicitly defined by some characteristics. It was previously known that there was a relationship between them, but it was not suspected that there were, in fact, equal.

Considerable work is required to understand what these are, and what the result means.

And to answer your explicit question, yes, the reals can be put in 1-1 correspondence with 2^N, the power set of the naturals.