The equation 1 = 2

a = b a^2 = ab  a^2 - b^2 = ab - b^2 (a - b)(a + b) = b(a - b)  (a - b) (a + b) = b (a - b)  (a + b) = b  but a = b  therefore: a + a = a 2a = a  hence 2 = 1

there is a calculus version of the equation which may be done later.