A: NUMBER
Symbols used to represent numbers are called digits. Example: 0, 1, 2, 3, 4, 5, 6. Expressions formed by combining digits in quantity are referred to as numbers.
Note: Every digit is a number, but some numbers are not digits.
B. NUMBER SETS
1. Counting Numbers: Each element of the set {1, 2, 3, …, n, …} is called a counting number.
2. Natural Numbers: Each element of the set {0, 1, 2, 3, …, n, …} is called a natural number. Natural numbers are represented by .
Positive Natural Numbers= {1, 2, 3, 4, … , n , …} = Each element of the set {1, 2, 3, 4, …, n, …} is called a positive natural number and is represented by .
Note: Each element in the set of counting numbers is also called a positive natural number.
3. Integers: Each element of the set {…, -n, …, -3, -2, -1, 0, 1, 2, 3, …, n, …} is called an integer and is represented by .
The set of integers is union of the set of negative integers: and the set of positive integers:
and zero {0} . Therefore,
4. Rational Numbers: Numbers that can be written in the form , where a and b are integers and b is not zero, are called rational numbers and are represented by
5. Irrational Numbers: Numbers that are not rational are called irrational numbers. Irrational numbers are those whose decimal representations do not follow a specific pattern. The set of irrational numbers is represented by . Therefore, The elements of the set
cannot be represented as
. (a, b
and b
0)
Note: There is no number that is both rational and irrational. ,
,
,
,
are examples of irrational numbers.
6. Real Numbers: The set of real numbers is the union of the set of rational numbers and the set of irrational numbers, and it is represented by