The collection of integers is the set of whole numbers and their opposites, including zero.
Integers encompass all positive whole numbers (1, 2, 3,...), all negative whole numbers (-1, -2, -3,...), and zero (0). They can be represented on a number line extending infinitely in both positive and negative directions.
Representation of Integers
The set of integers is typically denoted by the symbol Z (from the German word Zahlen, meaning "numbers"). This set can be written as:
Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}
Key Characteristics of Integers
- Whole Numbers: Integers consist only of whole numbers; they do not include fractions or decimals.
- Positive and Negative: Integers include both positive and negative numbers.
- Zero: Zero is an integer, and it is neither positive nor negative.
- No Fractions or Decimals: Integers do not include any fractional or decimal parts.
- Infinite Set: The set of integers is infinite, extending endlessly in both positive and negative directions.
Examples of Integers
- -5
- 0
- 7
- -100
- 1000
Non-Examples of Integers
- 1.5 (decimal)
- 1/2 (fraction)
- √2 (irrational number)
Practical Applications
Integers are fundamental in various mathematical and real-world applications, including:
- Accounting: Representing profits (positive integers) and losses (negative integers).
- Temperature Measurement: Representing temperatures above and below zero degrees.
- Elevation: Representing altitudes above and below sea level.
- Computer Science: Representing data and performing calculations in computer programs.
In summary, the collection of integers is a foundational number system comprising all whole numbers, their negative counterparts, and zero, playing a vital role in mathematics and numerous practical fields.
