I have another intresting theorm that proves 1 = 2.
let a = b
hence, a2 = ab ------ (multiplying both sides by a)
hence, a2 - b2= ab - b2 ------ (subtracting b2 from both sides)
hence, (a+b)(a-b) = b(a-b) -------(factorizing)
hence, (a+b) = b
but since a = b we get,
a + a = a ------ (replacing b by a)
hence, 2a = a
hence 2 = 1 or 1 = 2