Jagdish's Page for international Education

Lalit from Delhi started preparing for GRE recently. His confusion with numbers (as written by him in the forum) is the reason for this post. "Lalit, I hope this post provides the basic definition of numbers".

While studying arithmetic and algebra, we work with several groups of numbers.

NATURAL or COUNTING NUMBERS: The numbers 1, 2, 3, 4, . . . are called natural or counting numbers .

WHOLE NUMBERS : The numbers 0, 1, 2, 3, . . . are called whole numbers.

INTEGERS: The numbers . . . — 2, -1, 0, 1, 2, . . . are called integers .

NEGATIVE INTEGERS : The numbers . . . — 3, —2, -1 are called negative integers .

POSITIVE INTEGERS : The natural numbers are sometimes called the positive integers .

RATIONAL NUMBERS: Fractions, such as 3/2 or 7/8, are called rational numbers. Since a number such as 5 may be written as 5/1 all integers are rational numbers .

IRRATIONAL NUMBERS : Another type of number is an irrational number. Examples of irrational numbers are square root of any natural number or say for example pie .

REAL NUMBERS: Real numbers consist of all rational and irrational numbers. Typically most standardized exams use only real numbers ,which are the numbers you are used to using .

PRIME NUMBERS : A prime number is a number that can be evenly divided by only itself and 1 . For example, 19 is a prime number because it can be evenly divided only by 19 and 1, but 21 is not a prime number because 21 can be evenly divided by other numbers ( 3 and 7) . The only even prime number is 2 ; thereafter, any even number may be divided evenly by 2 . Zero and 1 are not prime numbers. The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 .

ODD NUMBERS : Odd numbers are whole numbers not divisible by 2 :-1,3,5,7, . . .

EVEN NUMBERS : Even numbers are numbers divisible by 2:- 0, 2, 4 ,6, . . .

COMPOSITE NUMBERS: A composite number is a number divisible by more than just 1 and itself: 4, 6, 8, 9, 10, 12, 14, 15, . . .

SQUARES: Squares are the result when numbers are multiplied by themselves : (2 . 2 = 4), (3 • 3 = 9) ; 1, 4, 9, 16, 25, 36 . . .

CUBES: Cubes are the result when numbers are multiplied by themselves twice: (2 . 2 . 2 = 8), (3 • 3 . 3 = 27) ; 1, 8, 27 . . .