Hi everyone. This post is about numbers and the number system in mathematics.
Sections
- Natural Numbers
- Non-Negative Integers
- Integers
- Rational Numbers (Fractions)
- Irrational Numbers
- Real Numbers
- Extension: Complex Numbers
Natural Numbers
The natural numbers refer to the positive whole numbers from 1 and going up. You could see them as counting numbers starting from 1. The set of all natural numbers is denoted by a funny looking N.
Non-Negative Integers
The non-negative integers is just an extension of the natural numbers. Instead of counting from 1, we start counting from 0 and then go up. The set of non-negative integers is {0, 1, 2, 3, 4, ... }.
Integers
When negative whole numbers are added to non-negative integers, we get the integers. The set of integers is denoted by a weird looking Z.
Rational Numbers (Fractions)
Many of us are familiar with the concepts of fractions. Fractions can also be referred to as rational numbers. A fraction/rational number contains an integer in the numerator (top) and a non-zero integer in the denominator (bottom). The set of rational numbers (fractions) is denoted by a strange looking Q.
This is the math version of saying that a and b are integers where the bottom cannot be zero (Dividing by zero is a math crime!).
Integers are considered rational numbers as the denominator/bottom of a fraction is simply 1 (b = 1).
Irrational Numbers
A number that is not rational (but still real) is irrational. Irrational numbers are not fractions and contain a never ending amount of decimal places. Examples include:
(Edit On Aug 12, 9:20PM EST: Fixed the golden ratio number typo. )
Real Numbers
All of the numbers (including the irrationals) from the previous sections belong to the real numbers. The real numbers is denoted by 
.
Extension: Complex Numbers
This particular concept may not be suitable for younger students. (You could just tell them that you cannot take the square root of a negative number as it is not a real number.)
Remember when a (high school) math teacher told you that a square root of a negative number is not real? It belongs to the set of complex numbers. The set of complex numbers is denoted by a weird looking C like this: 
.
A complex number contains a real number part and an imaginary number part. The form of a complex number is:
where
a is a real number
b is a real number
i is an imaginary number with 
.
Complex numbers are used in fields such as physics, electrical engineering, fluid dynamics and certain math fields. I am not an expert on complex numbers so it is best to ask others who are familiar with complex numbers.
Here is another summary image but with the complex numbers.
