What type of numbers make up a real number?

Start with the natural numbers, 0, 1, 2, ... .Then add the set of negative numbers: this makes up the integers.

Next add in the set of ratiOS of any two integers (the second being non-zero): this makes up the rational numbers.

Next add in the set of all numbers which cannot be expressed as terminating or repeating decimal numbers. This is the set of Irrational Numbers.

The rationals and irrationals, together, make up the set of real numbers.