Real Numbers

1. Real numbers are a combination of rational and irrational numbers.
2. real numbers can be represented in the number line and these have a fixed point in the number line. 
3. Real
   numbers have four properties, commutative property, associative property, distributive property, and identity property. Consider “a, b
   and c” are the real numbers. Then based on these properties, we can
   define the numbers as; 

• Commutative property : 
• If we have ‘a’ and ‘b’ two numbers, then a+b = b+a  for addition and a×b = b×a for multiplication.
• i.e addition : 2+3 = 3+2 return 5 in both sides.
•      multiplication:  2×3 = 3×2 returns 6 in both sides.

• Associative property:
• for these 3 numbers a,b and c,  a+(b+c) = b+(c+a) for addition and a×(b×c) = b×(c×a) for multiplication.
• i.e. 2+(3+5) = 3+(5+2)  addition
•   2×(3×5) = 3×(2×5) multiplication

• Distributive property : 
• for these 3 numbers a,b,and c,  ( a×(b+c) = a×b + b×c ) ,  i.e. 2×(3+5) = 2×3 + 2×5  returns 16 in both sides.

• Identity property :
• There are additive and multiplicative identities :
• for a real numbers ‘a’ , a + 0  = a , (here 0 is the additive identity).
• and a × 1 = a ( here 1 is multiplicative identity). 

1. The set of real numbers includes all the natural numbers, fractions, and decimals. 
2. Real numbers are represented by ‘R’.
3. Examples of real numbers are : 6,4.5,3/2, π(3.14) , -14 etc.
4. imaginary numbers are the non-real numbers and represent a complex number which can’t be located on a number line