Logical reasoning problem. I believe this \'fuzzy math\' is possible because if

Question

Logical reasoning problem. I believe this 'fuzzy math' is possible because if A and B are replaced by any integer divisible by two, 2 can equal 1. Just trying to see if my head is in the right place.

If A = B --> Multiply both sides by A --> A2 = AB

Subtract B2 from both sides --> A2 – B2 = AB – B2

Factoring each side gives --> (A + B) (A – B) = B (A-B)

Divide both sides by (A – B) --> A + B = B

And since A = B --> B + B = B Or 2B = B

Divide both sides by B, and

2 = 1   

How is this possible?

Explanation / Answer

At this step, (A + B) (A – B) = B (A-B) , we CAN NOT take a term common out.

Because, A2 – B2 = AB – B2 which literally implies, 0-0 = 0-0 . From this notation, you can NOT proceed with the other step which is giving (A+B) 0 = B X 0 As you should not common out something when there is nothing. i.e 0.

Eg: 5 x 0 = 6 x 0 But you can not cancel out 0 and write 5 = 6 right?

Hope this helps!

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