What are integers? What are positive integers? This article will give you the answers.
What are integers? What are positive integers? This article will give you the answers.
In mathematics, there are many sets of numbers such as the set of natural numbers, the set of integers, mixed numbers , real numbers , etc. This article will introduce you to the set of integers so that you can understand what integers are, what positive integers are, what negative integers are, and how integers differ from other sets of numbers. Please refer to the following information.
What are integers?
In mathematics, integers are the set of whole numbers and negative numbers. Similar to integers, integers also do not include fractions. Therefore, we can say that integers are numbers that can be positive, negative, or zero, but cannot be fractions. We can perform all arithmetic operations, such as addition, subtraction, multiplication, and division, on integers. Examples of integers are 1, 2, 5, 8, -9, -12, etc. The symbol for integers is 'Z'. Now, let's discuss the definition of integers, their notation, type, operations on integers, rules and properties related to integers, and how to represent integers on a number line with many detailed examples.
- Non-zero natural numbers are also called positive integers (sometimes written as +1, +2, +3,…but the '+' sign is usually omitted).
- The numbers -1, -2, -3,… are negative integers.
- The set of integers includes: {.; -3; -2; -1; 0; 1; 2; 3;.}
Note:
- The number 0 is neither a negative integer nor a positive integer.
- The point representing the integer a on the number line is called point a.
Properties of the set of integers
Integers belonging to the set Z will have the following basic properties:
- There is no such thing as the largest or smallest integer. The concepts of largest and smallest are relative and depend on the conditions in each case.
- The smallest positive integer is 1. The largest negative integer is -1.
- The integer Z comprises an infinite number of finite subsets. These subsets will contain a defined minimum and maximum integer.
- There is no integer that lies between two consecutive integers.
Opposite number
On the number line, the points 1 and -1, 2 and -2, 3 and -3, . are equidistant from point 0 and lie on opposite sides of point 0. We say that the numbers 1 and -1, 2 and -2, 3 and -3, . are opposite numbers.
The opposite of zero is 0.
For example:
- The numbers 10 and -10 are opposite numbers.
- The number 110 and the number -110 are opposite numbers.
How do we represent integers on a number line?
Since we've discussed three types of integers, we can easily represent them on a number line based on positive integers, negative integers, and zero.
Zero is the center of the integers on the number line. Positive integers are to the right of zero, and negative integers are to the left. See the image below.
Hopefully, the above article has helped you understand what integers are and what set of numbers Z represents.