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

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

  1. krecksteegh reblogged this from visualizingmath
  2. yourtormentandpleasure reblogged this from visualizingmath
  3. firsttimetumblerlongtimefaller reblogged this from bloodyhellwoman
  4. encyclopediac reblogged this from lootibles
  5. homeystucks reblogged this from frayofsherwood
  6. frayofsherwood reblogged this from lal-nila-syrin
  7. just1hour reblogged this from visualizingmath and added:
    Love it!!!!!!!!!
  8. swedish-mathematician reblogged this from icypiece and added:
    Well .. actually division won’t help you at all in getting from Whole Numbers to Integers. Only subtraction will help....
  9. icypiece reblogged this from mistyaiya
  10. becspresso reblogged this from mistyaiya
  11. mistyaiya reblogged this from visualizingmath
  12. bloodyhellwoman reblogged this from physicsshiny
  13. bo0tzz reblogged this from visualizingmath
  14. asiancanuck reblogged this from visualizingmath
  15. scenariot reblogged this from throughascientificlens
  16. quantumbanana reblogged this from visualizingmath
  17. glowstickia reblogged this from lal-nila-syrin
  18. enharbor reblogged this from thespacegoat
  19. themathdepot reblogged this from visualizingmath
  20. witchofvessalius reblogged this from lal-nila-syrin
  21. lal-nila-syrin reblogged this from thegreatyuil
  22. cronusamporaa reblogged this from visualizingmath
  23. kathaderon reblogged this from visualizingmath