Real Numbers

Real numbers are rational numbers plus irrational numbers.

Since rational numbers include integers and fractions, then real numbers include:

  • integers {..., -5,-4,-3,-2,-1,0,1,2,3,4,5,...}
  • fractions (proper, improper, mixed numbers)
  • irrational numbers (like `sqrt(2)`, `root(3)(-15)`, `pi`, `e` etc.)

Set of real numbers, i.e. group of real numbers, is denoted by `RR`.

As we already saw, all these numbers can be placed on a number line, which is called real number line.

real number line

Real numbers are called "real", because they are used in math to represent something:

  • `pi` is used to describe the ratio of circumference of any circle and its diameter
  • `sqrt(2)` is used to describe diagonal of unit square
  • `5/7` is used to describe 5 pieces of cake, that is divided into 7 pieces.