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 2\sqrt{{{2}}}, 153{\sqrt[{{3}}]{{-{15}}}}, π\pi, e{e} etc.)

A set of real numbers, i.e. a group of real numbers, is denoted by R\mathbb{R}.

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:

  • π\pi is used to describe the ratio of circumference of any circle and its diameter
  • 2\sqrt{{{2}}} is used to describe diagonal of unit square
  • 57\frac{{5}}{{7}} is used to describe 5 pieces of cake, that is divided into 7 pieces.