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 $20 \times 21$ 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 $(20 + 2) \times 19 = 418$ and a small one with area just over $2 \times 2 = 4$. 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 is in the above argument ?