The mathematical fallacy 2 = 1 is a classic one, guess which step is incorrect:
Let x = y.
Multiply by x: x² = xy.
Subtract y²: x² − y² = xy − y².
Factorize: (x − y)(x + y) = y(x − y).
Divide by (x − y): x + y = y
Because x = y, replace all x's with y's: y + y = y
Simplify: 2y = y
Divide by y: 2 = 1
Did you see the incorrect step? Spoiler alert: it's the fifth one; you can't divide by (x − y), as that equals 0 (because x and y are equal), and you can't divide by zero.
Let x = y.
Multiply by x: x² = xy.
Subtract y²: x² − y² = xy − y².
Factorize: (x − y)(x + y) = y(x − y).
Divide by (x − y): x + y = y
Because x = y, replace all x's with y's: y + y = y
Simplify: 2y = y
Divide by y: 2 = 1
Did you see the incorrect step? Spoiler alert: it's the fifth one; you can't divide by (x − y), as that equals 0 (because x and y are equal), and you can't divide by zero.
by Lakitu's Cloud December 10, 2014