Real Numbers: - The set of rational and irrational numbers together form a set of real numbers denoted by R.
Properties of Real Numbers :
1. Basic Properties: Let a,b,c are three real numbers
(i) Commutative law:
A. Commutative law for addition: a+b = b+a
B. Commutative law for multiplication: a.b = b.a
(ii) Associative Law:
A. Associative law for addition: (a+b)+c = a+(b+c)
B. Associative law for multiplication : a(b . c)=(a . b) . c
(iii) Distributive Law:
(a+b). c = a. c + b.c
(iv) Identity Law :
Let 0 and 1 are two real numbers, then
a+0 = a=a+0,
and a . 1 =1 . a = a
(v) Inverse Law
A. Additive inverse :
If a + (-a) = 0 = (-a) + a
Then -a is called additive inverse of a.
B. Multiplicative inverse:
If a x 1/a =1 = 1/a x a
then 1/a i.e. a-1 is called multiplicative inverse of a.
