I have recently stumbled upon this on a website and, along with several of my friends, have been trying to figure out if this is indeed valid or if there is a flaw somewheres in the mathmatics of it. Forgive me if it is something trivial for we have just graduated high school and may not have the knowledge needed to figure this out. Any help or explanation would be welcome. Here it is:
<prepared>Theorem: All numbers are equal.
<prepared>Proof: Choose arbitrary a and b, and let t = a + b. Then
<prepared>a + b = t
<prepared>(a + b)(a - b) = t(a - b)
<prepared>a^2 - b^2 = ta - tb
<prepared>a^2 - ta = b^2 - tb
<prepared>a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4
<prepared>(a - t/2)^2 = (b - t/2)^2
<prepared>a - t/2 = b - t/2
<prepared>a = b
<prepared>So all numbers are the same, and math is pointless.
(Copied from http://www.bash.org/?522860)