??

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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