Irrational Numbers (R)

Irrational numbers is the set of numbers that can only be aproximated in their decimal form (in a particular number system). They have a infinite amount of non-zero decimals (otherwise all floating-point numbers would be irrational). The square root of 2 is a simple way to demonstrate irrational numbers (in the decimal system).

The relationship between square root and exponents is as follows:

  1. $x^{\frac{m}{n}} = \sqrt[n]{x^m}$
  2. $\sqrt[2]{4^1} = 4^\frac{1}{2}$
  3. $\sqrt{2} = 1.4142135623730951...$
  4. $\sqrt{4} \in R$
  5. $\sqrt{2} \in R$
  6. $\sqrt{2} \notin Q$

Irrational numbers and it’s subsets are described as real numbers.