Classification of Numbers:
Natural Numbers: The numbers 1, 2, 3, 4, 5, 6, . . . . . . which we use in counting are known as natural numbers. The set of all natural numbers can be represented by N = {1, 2, 3, 4, 5, . . . . . . . . . .}
Whole Numbers: If we include 0 among the natural numbers then the numbers 0, 1, 2, 3, 4, 5, . . . . are called whole numbers. Hence, every natural number is a whole number. The set of whole numbers is represented by W.
Integers: All counting numbers and their negatives including zero are known as integers. The set of integers can be represented by Z or I. Z = {. . . . . . –4, –3, –2, –1, 0, 1, 2, 3, 4, . . . . .} Every natural number is an integer but every integer is not a natural number.
Positive Integers: The set I+ = {1, 2, 3, 4, . . . . .} is the set of all positive integers. Positive integers and natural numbers are synonyms.
Negative Integers: The set I– = {. . . , –3, –2, –1} is the set of all negative integers. 0 (zero) is neither positive nor negative.
Non Negative Integers: The set {0, 1, 2, 3, . . . } is the set of all non-negative integers.
Rational Numbers: The numbers of the form p/q, where p and q are integers, p is not divisible by q, and q ≠ 0, are known as rational numbers. Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions. The set of rational numbers is denoted by Q.
Irrational Numbers: Any real number that cannot be written in fraction form is an irrational number. Numbers which are both non-terminating as well as non-repeating decimals are called irrational numbers. Examples include the absolute value of √3, √2, √5.