Proof that 2 = 1

Proof.md

Let a = b

a^2 = ab
a^2 + a^2 = a^2 + ab
2a^2 = a^2 + ab
2a^2 - 2ab = a^2 + ab - 2ab
2a^2 - 2ab = a^2 - ab
2(a^2 - ab) = a^2 - ab
2 = 1

@brettberry see if you can figure this out

btw never, ever divide by a variable under any circumstance (common error I saw all the time with students)...it either results in a divide by zero error explicitly, or as in many algebraic equations results in losing the zero answer case (which is harder to detect) since when the variable takes on zero it breaks the equation. (eg say I have 2x = 3x, well if I divide by x I get 2 = 3, because the only real solution for x is 0; or more common x^2 - 2x = x, some students try this: x(x-2) = x -> x(x-2)/x = x/x -> x-2 = 1 -> x = 3; this is confusing because x = 3 is a correct answer (3^2 - 2*3 = 3) but so is zero (0^2 - 0 = 0), you lose the zero case. The correct way of solving would be to collect and factor so that all solutions remain present: x^2 - 3x = 0 -> x ( x - 3 ) = 0 -> x = 0 and x = 3.