Howdy everyone,

Here is a cute little 'proof.'

Obviously, this is bunk. So what is the mathematical mistake?Theorem: 4 = 5

'Proof':

-20 = -20 (obviously...)

16 - 36 = 25 - 45 (just two different ways to write -20)

4^2 - 9*4 = 5^2 - 9*5 (factoring...)

4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4 (add 81/4 to both sides)

(4 - 9/2)^2 = (5 - 9/2)^2 ("completing the square")

4 - 9/2 = 5 - 9/2 (get rid of the squares)

4 = 5 (cancel the 9/2 from both sides)

Have fun,

william