Number System Cheat Sheet

Key Definitions

• Natural Numbers: Counting numbers starting from 1 (1, 2, 3, ...). ✅

• Whole Numbers: Natural numbers including 0 (0, 1, 2, 3, ...). ✅

• Integers: Whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...). ✅

• Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. ✅

• Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., √2, π). ✅

Important Concepts

Types of Numbers

• Prime Numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves (e.g., 2, 3, 5). ✅

• Composite Numbers: Natural numbers greater than 1 that are not prime (e.g., 4, 6, 8). ✅

• Even and Odd Numbers: Even numbers are divisible by 2; odd numbers are not. ✅

Number Properties

• Closure Property: The sum or product of two integers is always an integer. ✅

• Associative Property: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). ✅

• Distributive Property: a × (b + c) = (a × b) + (a × c). ✅

Key Formulas

• L.C.M.: Least Common Multiple

• G.C.D.: Greatest Common Divisor

Common Mistakes to Avoid

Common Mistake: Confusing prime and composite numbers; remember that 1 is neither.

Memory Tricks

Tip: "SILVER" — Sum, Integer, LCM, Value, Even, Rational

Key Diagrams

   +-----+
   |  1  |  Natural Numbers
   +-----+
      |
   +-----+
   |  0  |  Whole Numbers
   +-----+
      |
   +-----+
   | -1  |  Integers
   +-----+
      |
   +-----+
   | 2/3 |  Rational Numbers
   +-----+
      |
   +-----+
   | √2  |  Irrational Numbers
   +-----+