10th Class Mathematics Real Numbers Real Number

         Real Number

Real numbers are the collection of rational and irrational numbers or In other words we can say that a number whose square is always non-negative, is know as real numbers.  

Note:

(i) There are infinite real numbers between any two distinct real numbers.

(ii)   

             Properties of Real Numbers

In this section we will study about addition and multiplication properties of real number.  

Addition Properties

(i) The sum of two real numbers is always real.

(ii) For any two real numbers A + B = B + A.

(iii) For any three real numbers A, B and C (A + B) + C = A + (B + C).

(iv) O is the additive identity of real number.

(v) For a real number (a), (-A) is the additive inverse.  

Multiplication Properties

(i) The product of two real numbers is always a real number.

(ii) For any two real numbers A and B, AB = BA.

(iii) For any three real numbers A, B and C, .

(iv) 1 is the multiplicative identity for every real number.

(v) For every non-zero real number A, is the multiplicative inverse.

(vi) For any three real numbers A, Band C