Quote: Originally Posted by Thorsen
Wrong: (a+b)(a-b)=a(a-b) (Equation 4)
Correct: (a+b)(a-b)= a^2-ab+ab-b^2 = a^2-b^2
Another Edit: This is done in many forms to try and prove that 1=0, but it is at this point that I always see this failure.
Likewise, the formula "(a+b)(a-b)= " deontes, that there are two answers to the formula in that there are two possible outcomes a+b and a-b... thus two different answers for this fomula either subracting b or adding b. a will never yeild the same result unless b=0
I don't quite understand the last paragraph... Are you saying that the two terms in (a+b)(a-b) = ???? can only mean two roots? If so, there are many polynomials with a single root. Or more properly I guess two identical roots.
Actually Equation 4 is correct if
a=b... The biggest error comes in the following step.
if a=b then a-b=0 and equation 5 is derived by dividing both sides by zero, which is not defined.
Of course if a=b, equation 4 can be reduced to 0=0 which is perfectly valid, but applying undefined functions makes the proof invalid.