Introduction to Number Systems
ch1-introduction
Rational Numbers
ch1-rational-numbers
Exercise 1.1 - Detailed Solutions
ch1-exercise-1-1
Irrational Numbers
ch1-irrational-numbers
Exercise 1.2 - Detailed Solutions
ch1-exercise-1-2
Real Numbers & Decimal Expansions
ch1-real-decimals
Exercise 1.3 - Detailed Solutions
ch1-exercise-1-3
Operations on Real Numbers
ch1-operations
Rationalizing the Denominator
ch1-rationalization
Exercise 1.4 & 1.5 - Solutions
ch1-exercise-1-4-5
Laws of Exponents for Real Numbers
ch1-laws-exponents
Chapter 1 Summary
ch1-summary
What is a Polynomial?
ch2-introduction
Types of Polynomials
ch2-types
Zeroes of a Polynomial
ch2-zeroes
Exercise 2.1 - Detailed Solutions
ch2-exercise-2-1
Remainder Theorem
ch2-remainder-theorem
Factor Theorem
ch2-factor-theorem
Algebraic Identities
ch2-identities
Exercise 2.4 - Identity Applications
ch2-exercise-2-4
Chapter 2 Summary
ch2-summary
In this chapter, we will explore the fascinating world of numbers!
Numbers are organized in a beautiful hierarchy:
| Set | Symbol | Description | Examples |
|---|---|---|---|
| Natural Numbers | ℕ | Counting numbers | 1, 2, 3, 4, 5... |
| Whole Numbers | W | Natural + zero | 0, 1, 2, 3... |
| Integers | ℤ | Whole + negatives | ...-2, -1, 0, 1, 2... |
| Rational Numbers | ℚ | Can write as p/q | 1/2, -3/4, 5, 0.75 |
| Irrational Numbers | - | Cannot write as p/q | √2, π, e |
| Real Numbers | ℝ | Rational + Irrational | All above numbers |
The containment: ℕ ⊂ W ⊂ ℤ ⊂ ℚ ⊂ ℝ
This means every natural number is also a whole number, every whole number is an integer, and so on!
Interactive Visualization