Background
I have been recently searching for a good number diagram I could save for future reference. I was looking for a picture that would show different types or real numbers, and also differentiate between transcendental and algebraic numbers. I found a couple of decent pictures but none of them were "perfect" to me.
Let's take a look:
Ok, so this one is pretty decent, but it has 2 issues that were brought up here: Are there any non-algebraic, non-transcendental complex numbers? Is $0$ a pure imaginary number?. First, everything that's not algebraic (blue) is transcendental, but this picture shows only transcendental numbers that are also irrational and ignores the rest. Second, it does not acknowledge the fact that 0 is both real and pure imaginary. Also, I really don't like that natural numbers are called counting numbers here. Like, it's a pretty advanced diagram definitely not targeted at elementary school students, so just call it natural.
Here is another example:
This one is interesting. My main problem with it is that the Algebraic numbers rectangle is contained within the Complex numbers rectangle with Transcendental numbers floating around in such a way that it doesn't really show the dichotomy between algebraic and transcendental numbers. Also, natural numbers containing zero? No, this doesn't sit right with me.
My Question
Finally, here is what I created and what I propose to you:
Please, use it if you like it, and, please, let me know what you think. One issue that's still bugging me is what to do with the fact that $0$ is both real and pure imaginary. Are the vast majority of number diagrams on the Internet that show real and pure imaginary numbers as 2 completely separate bubbles wrong? Should they overlap at zero the way it's done on the second diagram?