Page 2: Intervals and Advanced Concepts

This page delves into przedziały liczbowe (numerical intervals) and additional mathematical concepts including prime numbers and percentages.

Definition: An interval is a set of all real numbers between two given numbers, which can be open (a,b), closed [a,b], or half-open [a,b) or (a,b].

Example: For interval notation:

• (a,b) means a < x < b
• [a,b] means a ≤ x ≤ b
• (a,∞) means x > a
• $-∞,b$ means x < b

Highlight: The relationship between Greatest Common Divisor (GCD) and Least Common Multiple (LCM): For any two natural numbers a and b, GCD(a,b) × LCM(a,b) = a × b

Definition: A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself.

The page concludes with important theorems about number properties and introduces percentage calculations, making it essential for understanding działania na przedziałach (operations with intervals).

Page 1: Introduction to Number Sets and Operations

This page introduces fundamental concepts of zbiory liczbowe liceum (number sets in high school) and basic set operations. The content covers essential mathematical notation and set relationships.

Definition: A set is a collection of elements denoted by capital letters (A, B, C), with elements written between curly brackets { }.

Vocabulary:

• Ø represents an empty set
• ∈ indicates set membership
• ⊂ denotes subset relationship

Example: Natural numbers (ℕ) = {0, 1, 2, 3, ...} Positive natural numbers (ℕ+) = {1, 2, 3, 4, ...}

Highlight: The relationship between different number sets follows the pattern: ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ

The page also covers działania na zbiorach (set operations):

• Union (A∪B): Elements belonging to either A or B
• Intersection (A∩B): Elements common to both A and B
• Difference $A\B$: Elements in A that are not in B