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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.

enter image description here

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?

enter image description here

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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.2012-10-20
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    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.2012-10-20
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    Related question: http://math.stackexchange.com/questions/216177/in-a-venn-diagram-where-are-other-number-sets-located2012-10-21
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    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.2012-10-21

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

enter image description here

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    Do not forget the outer rectangle for the **quaternions**!!2012-10-20
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    Can you draw it? I cannot understand it without a real diagram.2012-10-20
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    No. The boxes are not supposed to overlap unless they are clealy inside one another. Imaginary numbers and Real numbers are disjoint, but their union makes the complex numbers. Rational and Irrational numbers are disjoint, but their union makes the real numbers.2012-10-20
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    Sigur: working on it, and adding some characterizations.2012-10-20
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    The union of the imaginary and real numbers is not the complex numbers!!!2012-10-20
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    This gives the impression that the complex numbers are the union of the reals and the imaginaries, which is not true. Where is $1+i?$ It shouldn't be banished to the quaterions.2012-10-20
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    Yeah, would have been smarter to just give a link like Emmad. Also... am I right about $\mathbb{Q}$ being the smallest ordered field and if we take all the limit points of $\mathbb{Q}$ that are not in $\mathbb{Q}$ do we get all the irrationals?2012-10-20
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    Ross... I see what you're getting at (I think). I've long imagined the Complex numbers as the union of the Reals and Imaginaries, but it's more like the cartesian cross-product. I'm not sure how to draw that, though. Maybe make the Complex a bigger box, since both Imaginary and Reals are subsets?2012-10-20
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    Ok, how about now? I feel like I want to move that bracket for the Reals to the right hand side.2012-10-20
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    Much better now.2012-10-20
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    Totally schooled by Emmad's second link though. Upvoted.2012-10-20
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    @ToddWilcox, good idea since you put one above other and not on the right.2012-10-20
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    Imaginary numbers and real numbers are not disjoint. Their intersection is $\{0\}$.2012-10-20
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    Rahul: Good catch. Further edits will have to wait another day or two. In the meantime, Emmad's second link is still the best thing I've ever seen on the subject.2012-10-21
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    I'm embarassed to admit that I've never been presented a formal definition of the imaginary numbers, and therefore assumed that 0 is not imaginary, since it doesn't fit with the name "imaginary".2012-10-21
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    Somehow this came out big and low-res. I went ahead and included the octonions for completeness. I'm not aware of any further extensions of $\mathbb{C}$.2012-10-24
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    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.2012-10-24
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    Kevin, I hope everyone will agree that your comment attached here provides the appropriate level of completeness for the diagram. :) And you've answered my question of why we can't keep extending $\mathbb{C}$ the same way. Namely, we can! I'm going to assume but not attempt to prove at this time that the number of extensions is countable.2012-10-24
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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 $\{0\}$.2012-10-20
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    @RahulNarain, its nice that the two worlds have something in common ;)2012-10-20
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    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.2012-10-20
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    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.2012-10-20