??
A Proof That 2 = 1. Let A = B:
A = B
multiply by A on both sides:
A x A = A x B
subtract B x B from both sides:
A x A – B x B = A x B – B x B
factorise:
(A + B)(A – B) = B(A – B)
divide by (A – B) on both sides:
(A + B) = B
replace A with B:
B + B = B
factorise:
2B = B
divide by B on both sides:
2 = 1
Where lies the flaw in the logic?
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Answer
On line 4 we are dividing both sides by (A – B).
But we know that A = B, so A – B = 0.
Dividing by zero is undefined, so we are not allowed to do this.
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