Theory of Positive Integers

An exploration of the properties, relationships, and applications of positive integers in various mathematical contexts.

Introduction to Positive IntegersDivisibility and MultiplesPrime Numbers and Composite Numbers
Greatest Common Divisor and Least Common MultipleThe Fundamental Theorem of ArithmeticNumber Patterns and Sequences
Using Positive Integers in Everyday LifePositive Integers in TechnologyOrganizing Events and Schedules
Breaking Down Problems with FactorizationUsing Patterns to Predict and Solve
Introduction to Posi...Divisibility and Mul...Prime Numbers and Co...Greatest Common Divi...The Fundamental Theo...Number Patterns and ...Using Positive Integ...Positive Integers in...Organizing Events an...Breaking Down Proble...Using Patterns to Pr...
Advanced Topics

Number Patterns and Sequences

Discovering Patterns

Positive integers can form amazing patterns, like arithmetic sequences (adding the same number each time) and geometric sequences (multiplying by the same number each time).

Types of Sequences

  • Arithmetic: 2, 5, 8, 11, 14 (add 3 each time)
  • Geometric: 3, 6, 12, 24, 48 (multiply by 2 each time)

Why Patterns Matter

Finding patterns helps us make predictions, solve puzzles, and understand how things grow or shrink in real life.

Where Do We Use Them?

Patterns are used in music, art, science, and even nature!

Examples

  • Counting by 4: 4, 8, 12, 16.

  • Doubling numbers: 1, 2, 4, 8, 16.

In a Nutshell

Patterns and sequences help us see how numbers grow, change, and repeat.

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Using Positive Integers in Everyday Life