Proof that 2 = 1

This is a gem.

Take any two numbers that are the same, like 2 and (4/2), call them 'A' and 'B'.
Thus A=B

Start with identity A^2 - B^2 = A^2 - B^2.

Substitute for one A: A^2 - B^2 = A^2 - A*B

Factor both sides: (A-B)(A+B) = (A-B)A

Cancel the term (A-B): (A+B) = A

Substitute A = B: B+B = B

So: 2B = B

Cancel the B from both sides: 2 = 1

It's an oldie but a goodie.