# How do we draw the number hierarchy from natural to complex in a Venn diagram?

I want to make a Venn diagram that shows the complete number hierarchy from the smallest (natural number) to the largest (complex number). It must include natural, integer, rational, irrational, real and complex numbers.

How do we draw the number hierarchy from natural to complex in a Venn diagram?

Edit 1:

I found a diagram as follows, but it does not include the complex number.

My doubt is that shoul I add one more rectangle, that is a litte bit larger, to enclose the real rectangle? But I think the gap is too large enough only for i, right?

Edit 2:

Is it correct if I draw as follows?

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The complex numbers would simply surround the whole thing, while the reals should be split between the irrationals and rationals. So here the green part itself is irrational, while everything the green contains is real. – Robert Mastragostino Oct 20 '12 at 2:16
There are a lot of number systems between the natural and the complex numbers. Most of those will hardly be mentioned explicitly outside courses for math students, though. – Asaf Karagila Oct 20 '12 at 9:37
Related question: math.stackexchange.com/questions/216177/… – Martin Sleziak Oct 21 '12 at 6:52
ガベージ, Your second diagram is what I originally considered as a further edit to mine, but if we want to be totally accurate, there's a problem. See how the circles that represent $\mathbb{Q}$ and $\mathbb{R}$ have small slivers outside of {0} that intersect $\mathbb{I}$? Technically, we shouldn't have that. – Todd Wilcox Oct 21 '12 at 22:32

There is a good picture at: number-set-venn-diagram. For detailing Complex Numbers, you can see this one: Complex Numbers Venn Diagram.

You may decide to combine the two to get a very complex picture!

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The first link depicts real numbers and imaginary numbers as disjoint, while the second one shows (correctly, in my opinion) that their intersection is $\{0\}$. – Rahul Oct 20 '12 at 10:14
@RahulNarain, its nice that the two worlds have something in common ;) – NoChance Oct 20 '12 at 11:44
Sorry, is each set open? I mean that whether or not points on the boundary of the set (in this case the rectangle) are included. – kiss my armpit Oct 20 '12 at 16:15
In Venn diagrams, objects live within the boundaries not on the boundaries themselves (I think). The pictures are meant to show the general idea, something like a country's high level map. – NoChance Oct 20 '12 at 18:39

Emmad's second link is just perfect, IMHO. For something right in front of you, here's this:

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Do not forget the outer rectangle for the quaternions!! – Sigur Oct 20 '12 at 2:18
Can you draw it? I cannot understand it without a real diagram. – kiss my armpit Oct 20 '12 at 2:25
Sigur: working on it, and adding some characterizations. – Todd Wilcox Oct 20 '12 at 2:38
The union of the imaginary and real numbers is not the complex numbers!!! – Sean O'Brien Oct 20 '12 at 2:47
There's an infinite tower of larger non-associative real algebras in dimension powers of $2$ going on above $\mathbb{O},$ beginning with the sedenions $\mathbb{S}$, but they're of no use to anybody, as far as I know. – Kevin Carlson Oct 24 '12 at 3:16