I came across a puzzle where we need to determine the error in the following proof.
False Theorem. 420 > 422
Proof. We will demonstrate this fact geometrically. We begin with a 20 × 21 rectangle,which has area 420.Now we cut along the diagonal and slide the upper piece parallel to the cut until it has moved exactly 2 units leftward. This leaves a couple stray corners,which are 2 units wide and just over 2 units high. Finally, we snip off the two corners and place them together to form an additional small rectangle. Now we have two rectangles, a large one with area just over (20 + 2) × 19 = 418 and a small one with area just over 2 × 2 = 4. Thus, the total area of the resulting ﬁgure is a bit over 418 + 4 = 422. By conservation of area, 420 is equal to just a little bit more than 422.
Can someone please explain what the error in the above argument is ?