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A Proof That 2 = 1:
1. let x=y
X = Y
2. multiply by x on both sides
X*X = XY
3. subtract y*y from both sides
X*X - Y*Y = XY - Y*Y
4. factorise
(X+Y)(X-Y) = Y(X-Y)
5. divide by (x-y) on both sides
(X+Y) = Y
6. replace x with y
Y+Y = Y
7. factorise
2Y = Y
8. divide by y 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 (X-Y).
But we know that X = Y, so X - Y = 0.
We are not allowed to divide by zero as this is meaningless.
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