Number Systems

Number systems are numbers grouped in specific areas of mathematics. All numbers we work with, both real and imaginary, are complex.

Complex numbers are divided into real and imaginary numbers. Real numbers then branch out into rational and irrational numbers. Rational numbers branch into integers, then integers branch into whole numbers, and whole numbers branch into natural numbers. This page will discuss all categories aforementioned.

Real Numbers
Real numbers are numbers that do not involve i, the function for imaginary numbers. Examples of real numbers are 3, -8, e, and $$\pi\,$$.

Imaginary Numbers
Further reading: Imaginary Numbers

Imaginary numbers involve integers and i.


 * $$\sqrt{-3}\, = i\sqrt{3}\,$$


 * $$\frac{i}{2i}\, = \frac{1}{2}\,i$$


 * $$i = \sqrt{-1}\,$$

Imaginary numbers cannot be broken down any further, so it is its own little stub of a branch on the tree of complex numbers. How sad.

Rational Numbers
Rational numbers either repeat or terminate in decimals. They can each be expressed as a fraction.


 * $$\frac{1}{\infty\,}\, = 0.\bar{0}\,1$$


 * $$\frac{1}{7}\, = 0.142857142857142857142857142857...$$


 * $$\sqrt[3]{-216}\, = -6$$


 * $$\sqrt[3]{216}\, = 6$$

Irrational Numbers
Irrational numbers neither repeat nor terminate. They cannot be expressed as a fraction. Most of the real numbers are irrational.


 * $$\pi\, = 3.141592653589793238462643383279502884197...$$


 * $$\sqrt{5}\,$$

Irrational numbers cannot be broken down any further, so it is its own branch of the complex number tree. Again, how sad.

Integers
Refer to the coordinate plane. For integers, imagine the x-axis alone. That is a number line, the best way to depict integers.

Integers include negative numbers, zero, and positive numbers.


 * $$..., -3, -2, -1, 0, 1, 2, 3,...$$

Whole Numbers
Whole numbers do not include negative numbers. Sorry, $$-\infty\,$$.


 * $$0, 1, 2, 3, 4,...,\infty\,-1, \infty\,$$

Natural Numbers
Natural numbers are the numbers you usually count with. Zero is omitted in the natural number system. Sorry, 0.


 * $$1, 2, 3, 4,...\infty\,-1, \infty\,$$