## Irrational Numbers and The Proofs of their Irrationality

"Irrational numbers are those real numbers which are not rational numbers!" Def.1: Rational Number A rational number is a real number which can be expressed in the form of where $a$ and $b$ are both integers relatively prime to each other and $b$ being non-zero. Following two statements are equivalent to the definition 1. 1. $x=\frac{a}{b}$ is rational if and only if $a$ and $b$ are integers relatively prime to each other and \$…