Real Numbers

The set formed by rational and irrational numbers is the set of real numbers.

The real number is denoted by Any Real Number.

Real Numbers

With real numbers all operations can be performed, except for the root of an even index and negative radicand and division by zero.

Adding Real Numbers

Properties

1. Closure:

A + b PerteneceReal Number

2. Associative :

(a + b) + c = + (b + c)

3. Commutative :

a + b = b + a

4. Additive Identity:

a + 0 = a

5. Additive Inverse:

a + (−a)= 0

−(−a) = a

Subtracting Real Numbers

The difference of two real numbers is defined as the sum of the minuend plus the opposite of the subtrahend.

a − b = a + (−b)

Multipying Real Numbers

The rule of signs for the product of integers and rational numbers is still maintained with the real numbers.

Rule of Signs

Properties

1. Closure:

a · b PerteneceReal Number

2. Associative:

(a · b) · c = a · (b · c)

3. Commutative:

a · b = b · a

4. Multiplicative Identity:

a · 1 = a

5. Multiplicative Inverse:

Real Number Properties

6. Distributive:

The product of a number for a sum is equal to the sum of the products of this number for each of the addends.

a · (b + c) = a · b + a · c

Dividing Real Numbers

The division of two real numbers is defined as the product of the dividend by the reciprocal of the divisor.