1. The problem is to understand and classify different types of real numbers. 2. Real numbers include rational numbers (which can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$) and irrational numbers (which cannot be expressed as a simple fraction). 3. Rational numbers include integers, whole numbers, and natural numbers. 4. Irrational numbers include numbers like $\sqrt{2}$, $\pi$, and $e$ which have non-repeating, non-terminating decimal expansions. 5. Every real number is either rational or irrational, and the set of real numbers is the union of these two sets. 6. Examples: - $5$ is a natural number, whole number, integer, and rational number. - $-3$ is an integer and rational number. - $\frac{1}{2}$ is a rational number. - $\sqrt{3}$ is an irrational number. 7. Understanding these classifications helps in solving algebraic and calculus problems involving real numbers.