Title credit: u/AngelicDimsum

Inscrutable, excellent

Each number is represented as a circle which contains the numbers below it.

4 contains 1 2 3 and 4 (the set contains itself)

Within the containing circle: Top left is a single circle, so it is 1. Top right is 2, so its a circle with another circle in it. Bottom left is three, so it contains both the previous symbols for 1 and a 2. And the final number is 4, so it has all the previous circle diagrams in it.

I may be missing something but why would 4 contain 4 when 3 doesn't contain 3 and 2 doesn't contain 2?

Excellent question, the answer is you've now reached the end of my understanding of set theory

I think you were off by one? I think the single circle is more like zero, then the top right is 1, bottom left is 2, bottom right is 3, and the whole thing is 4.

Sometimes I think that after I die, I'm gonna confront whatever higher power type of consciousness that was in charge of this reality and I'm gonna ask "What the heck was the purpose of all that?"

And the answer is gonna be, "It was actually an off by one error" and I feel like it's gonna actually make sense at that point.

Now express -1/12 as a summation of null sets? It'd take a bit.

Isn't four {{{{{}}}}}? The diagram shows more than that.

That would make sense because the fist circle is a null set with nothing in it

It could be defined that way. But your set is in a way more difficult to resolve as it has only one element. In the diagram the number of elements (4 sets) of the set is equal to the number 4 i.e. a set defines a number by simply counting its elements.

There are probably some other nice properties if you define it that way.

No, that's not how it's implemented in zfs. Probably to make implementing the basic arithmetic operations easier.

Gotcha, thank you.

TIL, thanks.