Real Numbers

Real numbers

  We all are familiar with the number system . Here we discuss about the Real Numbers. Real numbers are those values which represents a point in a straight line, known as the real line.

History:

 Around 1000 BC the Egyptians used integers and simple fractions for basic  calculations. The use of irrational numbers was started in 600 BC. The concept of irrationality was implicitly accepted by early indian mathematicians.The Greek mathematicians realised the need for irrational numbers around 500 BC.

  The acceptance of zero, negative and fractional numbers was boosted  in the middle ages.  Firstly, the indian and chinese mathematicians took the whole responsibility. Then  the arabic mathematicians also joined them.

   In 16th century the use of decimal notation was started widely. The great mathematician Descartes introduced the term 'real' to describe the roots of a polynomial , distinguishing them from ''complex" ones in the 17th century.

  In 18th and 19th centuries the work on irrational and transcendental numbers had more  developed.

  This is a brief history of real numbers.

  Well, we know that, real numbers or the set of Real numbers (R), consists of the sets of Rational numbers, Irrational numbers , Integers, whole numbers.

         

                                                                              

  Now we will discuss about these numbers.

Rational numbers: These real number are such type that, they can be expressed in the form:p/q, where , p and q are both integers and q not equals to zero. 2/3, 3/5,0, 1...etc. point to be noted that: every integer is a rational number as it can be expressed as p/q  such that q not equals to 0. Here we also highlight that , p can be zero. So 0 is a rational number. 

Irrational numbers: These real numbers can not be expressed in the form: p/q, where p and  q are integers and q not equals to zero.                                          

                                Pi(π) is a well known irrational number. √2,√3 ...etc are also irrational numbers.

 The set of Rational numbers also consist of Integers and fractions.

Integers: The set of integers consists of positive integers{1,2,3,...} , negative integers {...-3,-2,-1} and zero. The number zero is also known as "zero integer". The set of positive integers are also called the natural numbers (N).  The set of numbers contains zero and the set of natural numbers is called whole numbers {0,1,2,3,...} .

                         At the end we are to think about the  fractions.which are also rational numbers. Actually the rational numbers excluding the integers are fractions. Generally a fractions is a part of a whole number. fractions are of three types: proper fractions (numerator<denominator) , improper fractions (numerator>denominator) and mixed fractions (combination of a whole number and a proper fraction).

This is the family of Real numbers.

  

 If you find out any incorrect information or know anything more about this , please write it in the comment section!