Integers are whole numbers with no fraction or decimal, represented on a number line. Terminology is not standardized, but common groupings include non-negative or positive integers, natural numbers, and negative integers. The set of all integers is symbolized by Z and includes zero, which paved the way for advanced mathematics.
There are many different ways to look at integers, and therefore many different ways to classify them into types. Integers are sometimes called “whole numbers,” referring to the fact that a whole number represents a number with no fraction or decimal. These numbers can be plotted on a number line and are not abstract, like the so-called “irrational numbers”. Three, for example, is an integer, while 5.87 is not, because it is represented with a decimal, nor is . π is an example of an irrational number.
One thing to keep in mind when talking about integers is that the terminology surrounding these numbers is not standardized in the math community. People may use the same term to refer to different sets of numbers, for example. For wiseGEEK readers in a math class, it is recommended that you follow the definition used by the instructor.
A common grouping are the non-negative or positive integers, of the set {1, 2, 3…}. This set extends to infinity, for those who have spare time and enjoy counting. Some people also include 0 in this set, although 0 is technically neither positive nor negative, for the set {0, 1, 2, 3…}. People may also use the term “natural numbers” to refer to the set of all positive numbers, with some people including the number zero in this term while others do not.
Another type of integer is a negative integer. Negative integers are found in the set {-1, -2, -3…}. The set of negative numbers is also infinite in nature. An example of a negative integer would be a number like -37 or -9.520.
The set of all integers, including positive numbers, negative numbers and the number zero, may simply be known as “integers”, although this can sometimes be confusing as some people may assume that it refers only to the set of positive numbers. In mathematics, the letter Z is sometimes used to symbolize the complete set of integers. Z stands for Zahren, the German word for “number,” reflecting the influence of German mathematicians on mathematical terminology. Z is an all-encompassing term that includes all numbers recognized as integers.
These numbers are the building blocks of mathematics. The set of positive integers, excluding zero, has been used by man for thousands of years. Zero is actually a relatively recent introduction to the world of mathematics and it has proven to be groundbreaking. The ability to represent zero paved the way for the development of advanced mathematics such as algebra.
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