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Irrational numbers

The opposite of a rational number is an irrational number. All real numbers which are not rational are irrational.

By definition, all irrational numbers are also real numbers.

An irrational number is a real number which can’t be written as a simple fraction of two integers.

The set of irrational numbers is usually represented by the symbol :

  • (cannot be expressed as a fraction of two integers)
  • (cannot be expressed as a fraction of two integers)
  • (cannot be expressed as a fraction of two integers)
  • (cannot be expressed as a fraction of two integers)
  • (rational)
  • (rational)
  • (rational)
  • (rational)
  • (rational)
  • (rational, can be simplified to )
  • (rational, can be simplified to )
  • (not a real number)

The decimal equivalent to an irrational numbers have non-terminating and non-repeating decimal.

This means that the digits after the decimal point go on forever without ending, and there is no repeating pattern in the digits (e.g. how is ‘completely random’).