User blog comment:Explorer 767/One Equals One Hundred/@comment-1024726-20091228003342

Duh.

Given that $$a = b$$, it can be proven that $$4000 = 1$$.

$$4000a = 4000b$$

$$a = b$$

$$4000a^2 = 4000ab$$ (multiplying  by  $$a$$)

$$ab = b^2$$  (multiplying  by  $$b$$)

$$4000a^2-ab = 4000ab-b^2$$  (combining  equations)

$$4000a^2-4001ab = -b^2$$  (subtracting  $$4000ab$$)

$$4000a^2-4000ab = ab-b^2$$  (adding  $$ab$$)

$$4000a^2-4000ab+ab = 2ab-b^2$$  (adding  $$ab$$)

$$4000a^2-4000ab+ab-b^2 = 2ab-2b^2$$  (subtracting  $$b^2$$)

$$4000a(a-b)+b(a-b) = 2b(a-b)$$  (factoring)

$$4000a+b = 2b$$  (dividing  out  $$a-b$$)

$$4000a = b$$  (subtracting  $$b$$)

$$4000 = 1$$  (dividing  by  $$a$$ and $$b$$)

$$Q.E.D.$$