**ecn-ec:ecn-pc:ecn-ed:vu@pur-ee.UUCP** (09/10/83)

Why have 6 lines: Here's an equivalent "proof" of only 3 lines (the fallacy is the obvious): (-1)(-1) = 1 * 1 sqrt(-1) * sqrt(-1) = sqrt(1) * sqrt(1) -1 = 1 !!!!!!!!!!!!!!!!!!!!!!!! Hao-Nhien Vu (pur-ee!vu)

**ecn-ec:ecn-pc:ecn-ed:vu@pur-ee.UUCP** (09/10/83)

[Addendum to previous followup] As to the second "proof": x**2 = x + x +....+ x (x times) only when x is a positive integer. How the hell do you differentiate in a non-continuum ? The definition of derivative is the limit as x-->Xo. How do you get it in the set of integers ? Hao-Nhien Vu (pur-ee!vu)

**ken@turtleva.UUCP (Ken Turkowski)** (09/20/83)

Regarding the proof that 2 = 1 via calculus, x^2 = x + x + ... + x (x times) 2x = 1 + 1 + ... + 1 (x times) 2x = x 2 = 1 What the author fails to see is that in the first expression, x is really a parameter, x^2 = x * x By the product rule for derivatives, d/dx { x * x } = 1 * x + x * 1 = 2 * x, not 1 * x Ken Turkowski CADLINC, Palo Alto {decwrl,amd70}!turtlevax!ken