are irrational numbers real numbers

Answer 1

Yes, irrational numbers are a subset of real numbers. Real numbers include both rational numbers (which can be expressed as the quotient of two integers, such as \( \frac{1}{2} \) or \(-3\)) and irrational numbers (which cannot be expressed as a simple fraction). Examples of irrational numbers include \(\sqrt{2}\), \(\pi\), and \(e\). These numbers cannot be represented as a finite or repeating decimal. Hence, all irrational numbers are indeed real numbers, but not all real numbers are irrational.