>[!summary] Irrational numbers are fractions of numbers that **cannot** be expressed two integers. >[!info]+ Read Time ⏱ **1 mins** # Definition Irrational numbers any fraction of numbers that **cannot** be expressed as fraction of two [[Integers|integers]](a,b) and the [[Greatest Common Divisor (gcd)|gcd]](a,b) is reduced to 1. Mathematically irrational numbers are denoted as: $\text{Irrational Numbers} = \frac{a}{b} \quad \text{no } a,b \in \mathbb{Z}\quad b \neq 0 $ You can find proof of irrational numbers through [[Proof by Contradiction (Indirect Proof)#Examples|proof by contradiction]] ## Examples The following are examples of irrational numbers: - $\pi$ - $\sqrt{2}$ - $e$ --- > 📚 Like this note? [Star the GitHub repo](https://github.com/rajeevphysics/Obsidian-MathMatter) to support the project and help others discover it! ---