piclist 2001\06\03\135116a >
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BY : Byron A Jeff email (remove spam text)

On Sat, Jun 02, 2001 at 08:03:04PM -0500, David VanHorn wrote:
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Dave,

You need some infinity training. Let's try a few examples:

1) What's the largest integer?
2) What's the value of 1/0?
2A) What's the value of 1/infinity?
3) What's the smallest real number larger than 0? (BTW that's the answer to
4) Pick any two real numbers. How many real numbers are between the two?
5) What's the last digit of PI?

It's a simple mathematical fact that once you start dealing with infinity
the rules change. You find your difference above in the same place as the
largest integer and the smallest number bigger than 0. The answer is
infinity and 0. The last one sounds incongruous, but true. That's the nature
of infinity. 1/infinity doesn't approch zero. It doesn't approximate zero. It
isn't infinitely close to zero. IT IS ZERO! EXACTLY ZERO!

There is no difference between 1 and .9 (repeating). Not in infantisimal
difference. No difference. They are the same number. Of course any attempt
to make an infinite value finite make it lose it's infiniteness.

All of this fuss is over trying to attribute infinity to an approximation.
We use approximations to gain understanding in our little finite minds!
But you have to cross over and realize that once something is defined as
infinite, it is no longer an approximation of anything. It's exact.
And the math that works on infinity fails once you express finiteness on it.

The best treatment on the subject I ever read was Issac Asimov's "Asimov on
Numbers". He has several essay's on the nature of infinity.

Just remember that whenever you're having an infinity discussion, that you must
bring the largest integer to the table. Once you know that integer, the rest
is easy.

BAJ

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<20010603134944.A23051@cleon.cc.gatech.edu>

In reply to: <4.3.2.7.2.20010602195732.00ced4f0@mail.cedar.net>; from dvanhorn@CEDAR.NET on Sat, Jun 02, 2001 at 08:03:04PM -0500