**The Relationship of Numbers**

Today I wanted to share something with you, it’s not complex, but I was reminded of it today in maths class and it struck me as beautiful and nice and I figured I’d remind you of it, too.

In the diagram above you can see there are six circles, each which a family of numbers assigned to it. What I find fascinating is the easy steps one can take to move from the most inner circle to the most outer.

Natural Numbers:

These were the first numbers we had and used as a species: 1, 2, 3, 4, etc.

Whole Numbers:

This is essentially the same as the natural numbers, but now one key number is included: 0.

Integers:

Using our whole numbers we can use division or subtraction to move to this new set which includes the negative numbers: -2, -1, 0, 1, 2

Rational Numbers:

These numbers can be made by dividing one integer by another. Note: the denominator cannot be zero in this function. Rational numbers include decimals. Eg. 2/4 = 0.5

Irrational Numbers:

This circle sitting on its lonesome is a group of numbers which cannot be written in simple fraction form. They are infinitely long and consist of non-repeating series of numbers. Examples of irrational numbers are pi, e and the square root of two.

Real Numbers:

All of these groups put together form a group which is designated ‘real numbers’. All of these numbers exist, so to say.

Imaginary Numbers:

One group which was left off this diagram is the imaginary numbers. These numbers, while they have real life applications, have no physical representation. Eg. the square root of negative one.

Photo courtesy of Real Numbers Unit