M1 - Review of Number Concepts
Review of Number Concepts 1. Types of Numbers Classifications Natural Numbers ($\mathbb{N}$): Counting numbers starting from 1 (1, 2, 3, …). Integers ($\mathbb{Z}$): Whole numbers, including negatives and zero (…, -2, -1, 0, 1, 2, …). Prime Numbers: Natural numbers greater than 1 with exactly two factors: 1 and themselves (2, 3, 5, 7, 11, …). Note: 1 is not prime; 2 is the only even prime. Square Numbers: Result of multiplying an integer by itself ($1, 4, 9, 16, 25, \dots$). Cube Numbers: Result of multiplying an integer by itself twice ($1, 8, 27, 64, 125, \dots$). Rational Numbers ($\mathbb{Q}$): Numbers that can be written as a fraction $\frac{a}{b}$ where $a, b$ are integers and $b \neq 0$. Includes terminating and recurring decimals. Irrational Numbers: Numbers that cannot be written as simple fractions (e.g., $\pi, \sqrt{2}, \sqrt{3}$). Their decimal expansions are non-terminating and non-recurring. Reciprocals: The reciprocal of a number $x$ is $\frac{1}{x}$. The product of a number and its reciprocal is always 1. ...