I meant "both rational and irrational numbers". Had problems with that
insert / delete mode on the keyboard.
From: Meyer Robert K GS-9 99 CES/CECT
[SMTP:[log in to unmask]]
Sent: Monday, March 12, 2001 2:07 PM
To: [log in to unmask]
Subject: RE: (VERY) OFF TOPIC - Map coloring
You're on the right track, Pat, especially with your second point.
Computers can't prove anything. Basically, because they can't do
(excuse the pun). They only deal with finite numbers, very big
numbers maybe, but still finite. And there are two types of
countable (like rationals that can be put into 1-to-1 correspondence
integers) and uncountable (like irrationals that can't, or reals
that are a
set with both rational and rational numbers).
From: [log in to unmask] [SMTP:[log in to unmask]]
Sent: Monday, March 12, 2001 1:33 PM
To: [log in to unmask]
Subject: Re: (VERY) OFF TOPIC - Map coloring
In a message dated 3/12/01 12:14:55 PM Eastern Standard
[log in to unmask] writes:
It is the job of the mathematicians is to
meant by "every case". That's done all the time. For
example, in poker, the
"odds" of getting five cards of the same suit is
the NUMBER of ways five randomly drawn cards can be
same suit, and
then dividing that number by the TOTAL NUMBER OF
five cards can be
drawn from a 52 card deck.
Yes, and if n colors are going to be used to color n shapes,
possibilities is n to the nth power. This really includes
including using only one of the n colors for all of the n
Most of these color arrangments are not going to meet the
Saaty calls correct k-coloring--that is, no two contiguous
same color. For his correct k-coloring, the limit is n!.
That is, n
Thus, for four color used on a basic four-shape module,
possible combinations of which only 24 are "correct."
Now here are my questions.
1) This sounds to me like it's leading into a problem in
called combinatorial algebra. So why does one need a
2) For each n in the number series, the nth power of n is an
So is n factorial. So the computer, if using brute force,
out of steam at some point, as it can't deal with an
testing "every" possibility.
3) What was wrong with de Morgan's proof, which was
seems to me
that he was on the right track, much more so than what
4) Maybe you should rethink your poker example. The number
there's a limit to the number of cards in a pack. There's no
number of shapes that can be on a map. That's why one has to
along the line of breaking a large map down into, say, units
shapes. How, exactly, did they compute the number of
and what did the number turn out to be? You keep assuring me
"gazillions," which I don't find very clear. I'm actually
how it was computed than what it turned out to be.