What are the properties of real numbers?

Aug 09, 2022, 16:45 IST

Real Numbers:

The totality of rational and irrationals forms the set R of all real numbers.

Properties of Real Numbers:

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

           (ii) The product of two real numbers is always real.

2. For any two real numbers a and b, we have:

      (i) a + b = b + a                                     [Commutative law of addition]

      (ii) a  b = b a                                    [Commutative law of Multiplication]

3. For any three real numbers a, b, c we have:

      (i) (a + b) + c = a + (b + c)                   [Associative law of addition]

      (ii) (a x b) x c = a x (b + c)            [Associative law of Multiplication]

4. For any three real numbers a, b, c we have:

      a(b+c) = ab + ac 

      (a + b) c = ac + bc          [Distributive laws of multiplication over addition]

What are the properties of real numbers pdf