1. The problem is to understand the different types of numbers and their classifications. 2. Numbers are broadly classified into several types: 3. Natural Numbers ($\mathbb{N}$): These are the counting numbers starting from 1, 2, 3, and so on. They do not include zero or negative numbers. \[ \mathbb{N} = \{1, 2, 3, 4, \dots\} \] 4. Whole Numbers ($\mathbb{W}$): This set includes all natural numbers plus zero. \[ \mathbb{W} = \{0, 1, 2, 3, 4, \dots\} \] 5. Integers ($\mathbb{Z}$): These are whole numbers and their negatives, including zero. \[ \mathbb{Z} = \{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\} \] 6. Rational Numbers ($\mathbb{Q}$): Numbers that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers, and $q \neq 0$. This includes terminating and repeating decimals. 7. Irrational Numbers: Numbers that cannot be expressed as a fraction of integers. Their decimal expansions are non-terminating and non-repeating, such as $\pi$ and $\sqrt{2}$. 8. Real Numbers ($\mathbb{R}$): The set of all rational and irrational numbers. 9. Complex Numbers ($\mathbb{C}$): Numbers that include a real part and an imaginary part, usually written as $a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit with $i^2 = -1$. This classification helps to understand the nature and properties of numbers in mathematics.