On Fri, 5 Nov 2004 at 09:44:49 in message
.com, Raul Ruiz
wrote:
Brush up on your math...
http://www.math.utah.edu/~alfeld/math/0by0.html

I may be out on limb here with modern high school math but I don't
really agree with everything there! Perhaps it is my great age! I try to
learn form what people tell me but it gets harder and harder. :-(

(Infinity + infinity) = infinity so I agree you cannot just subtract one
of them each side and say infinity = 0 !!!

What is (1 + 1/n)^n as n tends to infinity? (Clue: it's a very
important number - assuming I have not screwed up that expression at my
great age.)

As I understand it only under very special circumstances can infinities
can be cancelled out. But it is done in some esoteric equations.

What is tan(Pi/2)? Better still plot tan(theta).

Of course infinity cannot be treated as an ordinary number but it still
'exists' and you can compute larger and larger numbers as long as you
like.

What I did was to plot three points on a function which at one point
tends or goes to infinity.

Do you agree that 20/b gets larger and larger as b gets smaller and
smaller and that there is no point at which you can say that ends? I
can say with confidence that 20/0 is infinity and I can go on from that
to say that 20/0 = 40/0. What I cannot do is to infer from that that 20
= 40. But that is the nature of infinity. I know that dividing both
sides of equation by zero cannot be done with impunity either. I agree
that you cannot place a value on (infinity * 0) but I didn't want to do
that.

Let a = b
multiply both sides by b a*b = b^2
subtract a^2 from both sides a*b - a^2 = b^2 - a^2
therefore a*(b - a) = (b + a)*(b - a)
cancel (b - a) then a = b + a
but a = b therefore 1 = 2

But I expect you all know that one!

It's all good fun!
--
David CL Francis