Puzzle 66 - solution

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 The question was 

What is wrong with this proof ?

a=b
multiply both the sides by a     --1
a2 = ab 
add -b2 to both the side           --2
a2-b2 =ab-b2 
factorizing                                --3
(a+b)(a-b) = b(a-b) 
divide both the sides by (a-b)    ---4
a+b=b
Substituting a with b,              ---5
2b = b
Dividing both the sides by b    ---6
2 = 1
 
The problem is with step 4. When a is equal to b, a-b is zero. You can not divide numbers by zero because division is only defined for non-zero numbers.
 

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