Number Systems: A Foundation in Math

Number Systems: A Foundation in Math and Daily Life

• Number systems are fundamental for representing quantities, enabling precise expression in various contexts (e.g., counting apples, measuring distances).

Mathematical Concepts and Applications

• All mathematical concepts and formulas stem from the number system.
• From basic arithmetic to advanced mathematical fields, numbers are essential for reasoning and problem-solving.

Types of Numbers

• Counting Numbers: Positive integers starting from 1 (1, 2, 3...).
• Whole Numbers: Counting numbers plus zero (0, 1, 2...).
• Integers: Positive and negative whole numbers including zero (-3, -2, -1, 0, 1, 2, 3...).
• Rational Numbers: Numbers expressible as fractions (e.g., 3/4, -2/5).
• Irrational Numbers: Numbers not expressible as fractions (e.g., √2, π).
• Real Numbers: The combination of rational and irrational numbers.
• Even Numbers: Divisible by 2 (e.g., 2, 4, 6...).
• Odd Numbers: Not divisible by 2 (e.g., 3, 5, 7...).
• Prime Numbers: Divisible only by 1 and themselves (e.g., 2, 3, 5...).
• Composite Numbers: Having multiple factors (e.g., 4, 6, 8...).

Digital Systems and Representation

• Number systems are crucial for digital systems due to their use of binary representation (base-2).
• Computers utilize bits (0s and 1s) to process information based on number system principles.