An integer is a whole number; it can be positive, negative, or zero. It does not include fractions or decimals.
Understanding Integers
Integers are a fundamental concept in mathematics. They form the basis for many more complex number systems. The word "integer" comes from the Latin word "integer," meaning "whole" or "intact." This perfectly describes their nature as whole, undivided numbers.
- Examples of Integers: -3, -2, -1, 0, 1, 2, 3, 100, -5000, etc.
- Non-Examples of Integers: -2.5, 1/2, 3.14, 0.01, etc.
The set of integers is often represented by the symbol ℤ. They are infinitely extensive in both the positive and negative directions.
Integers in Practical Applications
Integers are used extensively in various fields, including:
- Computer Science: Representing data such as counts, indexes, and memory addresses. Integer overflow, when a calculation results in a number exceeding the maximum representable integer value, can cause errors in programs.
- Accounting and Finance: Tracking financial transactions, quantities of goods, and balances.
- Physics and Engineering: Measurements and calculations involving discrete quantities.
Key Characteristics of Integers
- Whole Numbers: They are not fractions or decimals.
- Positive, Negative, or Zero: They can be any of these three.
- Ordered Set: Integers have a defined order; for example, -5 < 0 < 5.
- Closure Under Addition and Subtraction: Adding or subtracting two integers always results in another integer.
The ability to represent both positive and negative quantities makes integers crucial for representing a wide range of values and situations. Their lack of fractional components makes them suitable for counting and indexing tasks.
