Real Numbers
- Real numbers are a combination of rational and irrational numbers.
- real numbers can be represented in the number line and these have a fixed point in the number line.
- Real
numbers have four properties, commutative property, associative property, distributive property, and identity property. Consider тАЬa, b
and cтАЭ 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├Чb = b├Чa for multiplication.
- i.e addition : 2+3 = 3+2 return 5 in both sides.
- multiplication: 2├Ч3 = 3├Ч2 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├Ч(b├Чc) = b├Ч(c├Чa) for multiplication.
- i.e. 2+(3+5) = 3+(5+2) addition
- 2├Ч(3├Ч5) = 3├Ч(2├Ч5) multiplication
- Distributive property :
- for these 3 numbers a,b,and c, ( a├Ч(b+c) = a├Чb + b├Чc ) , i.e. 2├Ч(3+5) = 2├Ч3 + 2├Ч5 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 ├Ч 1 = a ( here 1 is multiplicative identity).
- The set of real numbers includes all the natural numbers, fractions, and decimals.
- Real numbers are represented by ‘R’.
- Examples of real numbers are : 6,4.5,3/2, ╧А(3.14) , -14 etc.
- imaginary numbers are the non-real numbers and represent a complex number which can’t be located on a number line
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