Fascinating stuff.

BTW, the referenced article is well-written and accessible, I think. It only explains the first two levels of infinity, but that's enough to show that infinity is not one single entity. I'm not generally very impressed by scientific writing on the net--it's often written by journalists/writers who don't really understand what they're talking about. But these two writers both know their topic and can explain it clearly.

They do a good job of bridging the deep theoretical and exploratory nature of mathematics along with a writing style that makes it approachable to even someone like me.

And then there are the references/cites for those that can dig deeper!

'hvn_nbr_2'? Seems there must be a story behind your handle.

I was previously only slightly aware of Quanta. After looking at the list of articles by the two authors of this one, I want to look at more.

About my handle hvn_nbr_2: It means "heaven number 2." I once wrote a book with my very different, very progressive view of the book of Revelation in the Bible. Originally, the book's title was going to be "Heaven Number 1 or Heaven Number 2?" That's because I see the "action part" of Revelation as a story that begins with one scene of heaven (very primitive, Bronze Age concepts) and ends with a completely different kind of heaven (very progressive). The whole story between the two scenes of heaven tells symbolically the past, present, and future of the Judeo-Christian tradition's long term gradual transformation from earliest Bronze Age ideas to a much more progressive, inclusive, and loving future. Hvn_nbr_2 means that I choose the more progressive views. Some time ago, I made several posts in the liberal Christians group with some of my thoughts on Revelation. (I'm avoiding giving more specific details about the book because I need to check out the DU TOS on such info.)

I can see how that makes some sense.

Now going off to learn some new stuff:
https://en.wikipedia.org/wiki/Three-age_system

I guess this system is quite different from the Christian bible one.

Suppose the contrary. Then there exists a sequence containing the decimal expansions of all real numbers between 0 and 1. Let x be a decimal expansion whose kth digit differs from that of the kth number in the sequence. Then x is not in the sequence, a contradiction.

I check Quanta Magazine several times a week..I like their science writing and its an innocuous non-profit that owns it.