Apologies, it appears that I killed off this message thread. It is an old math joke.
The error lies in the step "Cancelling out the common factor". The problem is that the common factor (A-B) is equal to zero and in "cancelling it out", we divided by zero. That, dividing by zero, is not allowed in mathematics and invalidates everything that follows.
tairving wrote:
So now a bit of algebra for you:
A=1 and B=1
Thus,
A = B
Multiplying both sides by A,
A^2 = AB
Subtracting B^2 from both sides,
A^2 B^2 = AB - B^2
Factoring,
(A+B)*(A-B) = B*(A-B)
Canceling out the common factor (A-B),
A+B = B
And, since A=1 and B=1,
2 = 1
How can this be?