BailiffQuimby
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- Feb 22, 2013
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What follows is a proof that 1 = 2. Since we know that 1 does NOT equal 2, there is obviously an error in the proof. Your job is to identify it. It requires a year of high-school algebra, so anyone who has at least learned to factor should be able to give it a try.
If you've heard it before, just keep quiet and let others give it a shot. No spoilers please if you already know the answer.
Start with two variables A and B such that they are equal. So:
A = B
Multiply both sides by A:
A^2 = AB
Subtract B^2 from both sides:
A^2 - B^2 = AB - B^2
Factor each side - the left using the difference of two squares,
and the right using greatest common factor:
(A + B) (A - B) = B (A - B)
Divide both sides by (A - B) to cancel it out
A + B = B
Substitute, replacing A with B, since we began by declaring them to be equal numbers
B + B = B
Combine like terms
2B = B
Divide both sides by B to cancel them out
2 = 1
So what did I do wrong?
If you've heard it before, just keep quiet and let others give it a shot. No spoilers please if you already know the answer.
Start with two variables A and B such that they are equal. So:
A = B
Multiply both sides by A:
A^2 = AB
Subtract B^2 from both sides:
A^2 - B^2 = AB - B^2
Factor each side - the left using the difference of two squares,
and the right using greatest common factor:
(A + B) (A - B) = B (A - B)
Divide both sides by (A - B) to cancel it out
A + B = B
Substitute, replacing A with B, since we began by declaring them to be equal numbers
B + B = B
Combine like terms
2B = B
Divide both sides by B to cancel them out
2 = 1
So what did I do wrong?