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, GCDa,b × LCMa,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).