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Number System

Suvam Banerjee
06 Mar 0 0

Natural Numbers: The set of counting numbers is called natural numbers. It is denoted by N, where N = {1,2,3, …..}

Whole Numbers: when zero is included in the set of natural numbers, then it is a set of whole numbers. It is denoted by W, where W = {0,1,2, …..}

Integers: When in the set of whole numbers, natural numbers with the negative sign are included, then it becomes a set of integers. It is denoted by Z, where Z = {-…. , -2, -1, 0, 1, 2, …..}

Integers can be divided into negative and positive integers.

Prime Numbers: The natural numbers which have no factors other than 1 and itself are called prime numbers.

Co-prime Numbers: Two numbers that have no common factor except one are called co-prime numbers. Example: 11 and 18 etc.

Rational Numbers: The numbers that can be expressed in the form of p/q where p and q are integers and co-prime are called rational numbers. It is denoted by Q. Rationalnumbers can be positive or negative.

Irrational Numbers : The numbers which are not rational numbers, are called irrational numbers. or π = 3.141592 is an irrational number.

Real Numbers : Set of all rational numbers as well as irrational numbers are called real numbers. The square of all real numbers is positive.

Some important points on numbers :

  • 2 is the only even prime number.
  • Number 1 is neither divisible nor prime.
  • Two consecutive odd prime numbers are called prime pair.
  • All natural numbers are whole, rational, integer and real.
  • Fractions are rational.
  • 0 is neither negative(-) nor positive(+) number.
  • Dividing any number by 0 gives infinity () whereas dividing 0 by any number gives 0.
  • The sum and product of two rational numbers is always a rational number.
  • The product and sum of a rational number and irrational number is always an irrational number.
  • There can be infinite numer of rational and irrational numbers between two rational numbers and two irrational numbers.

 

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