[net.math] -1 = 1, and 1 = 2 "proofs"

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