I remember of this image I've learned at school:
I've heard about other number (which I'm not really sure if they belong to a new set) such as quaternions, p-adic numbers. Then I got three questions:
- Are these numbers on a new set?
- If yes, where are these sets located in the Venn diagram?
- Is there a master Venn diagram where I can visualize all sets known until today?
Note: I wasn't sure on how to tag it.
Best Answer
This Venn diagram is quite misleading actually.
For example, the irrationals and the rationals are disjoint and their union is the entire real numbers. The diagram makes it plausible that there are real numbers which are neither rational nor irrational. One could also talk about algebraic numbers, which is a subfield of $\mathbb C$, which meets the irrationals as well.
As for other number systems, let us overview a couple of the common ones:
Now, note that this diagram is not very... formal. It is clear it did not appear in any respectable mathematical journal. It is a reasonable diagram for high-school students, who learned about rationals and irrationals, and complex numbers.
I would never burden [generic] high-school kids with talks about those number systems above.