Integers are a set of whole numbers that include both positive and negative numbers, as well as zero. They are part of the number system widely used in mathematics, representing quantities used in counting, measuring, and calculating. The term "integer" is derived from the Latin word "integrum," meaning "whole" or "untouched."
Integers are a discrete and infinite set, meaning they do not involve fractional or decimal parts. They consist of the numbers {..., -3, -2, -1, 0, 1, 2, 3, ...}, including zero, and extend infinitely in both the positive and negative directions. They are denoted by the symbol "Z" and are represented on the number line as equally spaced points.
Integers serve as a fundamental concept in various areas of mathematics, including algebra, number theory, and arithmetic. They are used in calculations involving addition, subtraction, multiplication, and division. The operations of addition and subtraction involve combining or taking away integers, while multiplication and division entail repeated addition or grouping.
Integers possess unique properties, such as closure under addition, subtraction, and multiplication. When two integers are added, subtracted, or multiplied, the result is always another integer. However, division of integers may result in a fractional or decimal value, which is not considered part of the set of integers.
Additionally, integers have an important property known as the ordering property. This property states that any two distinct integers can be arranged in a specific order on the number line to determine which one is greater, less, or equal to the other.
