Real Number

A real number is any number that can be expressed in decimal form. Real numbers includes both rational numbers and irrational numbers and nothing more. Real numbers are all number that you can find on a single axis:

Real numbers on axis

This goes both ways:

  • Every point on this axis represents a single real number. If you pick a point on the axis, it represents one real number. No more, no less.
  • Every real number has a single point on the axis. You cannot find a real number that cannot be expressed as a point on this axis.

We denote the set of real number as .

Properties of Real Numbers

  • Real number are closed under addition, subtraction, multiplication and division with exception of division by zero. It means that you can:
    • Add two real numbers and you always get a real number, e. g. 10 + π is a real number.
    • Subtract two real numbers and you always get a real number, e. g. 50 − √2 is a real number.
    • Multiply two real numbers and you always get a real number, e. g. is a real number.
    • Divide two real numbers and you always get a real number, e. g. 7/log23 is a real number.
    • The division by zero is not defined thus the result of 5/0 is not a real number in spite of both numbers 5 and 0 are real.
  • Real number are infinite and uncountable set.

You can meet real numbers in many other definition. See for example: