Post #15,263
10/26/01 11:48:26 AM
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Is it only the Finns....
who consider 1 a prime?
Don Richards,
Proud recipient of the ABBA.
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Post #15,281
10/26/01 2:23:53 PM
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Mathematicians argue about that one
And number theory papers which rely on exact counts often specify whether or not they consider 1 a prime. But most mathematicians I know tend to consider 1 a non-prime.
Another fun one is whether 0 is a natural number. That is one which people divide on according to their field. For instance people in combinatorics say it isn't. People in logic tend to say it is.
Of course most mathematicians think both of these questions are silly definitional issues, and wouldn't bother carrying on a serious argument about either of them...
Cheers,
Ben
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Post #15,288
10/26/01 2:39:12 PM
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So these are the math equivalent of the falling tree thing
My answer to the question re: falling tree, no witness, noise happens? is --
wait for it.....
shut up.
Don Richards,
Proud recipient of the ABBA.
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Post #15,300
10/26/01 4:00:59 PM
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enlighten me a little please
to me 0 is the midpoint of numbers. Positive integers go forward, negatives go forward in the opposite direction. So what is a definition of a natural number?
thanx,
bill
tshirt front "born to die before I get old"
thshirt back "fscked another one didnja?"
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Post #15,302
10/26/01 4:25:52 PM
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Natural number
A number without artificial flavoring of course.
Jay
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Post #15,305
10/26/01 4:34:50 PM
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AKA an Organic Number
-----
Steve
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Post #15,306
10/26/01 4:36:10 PM
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Free range digits?
Don Richards,
Proud recipient of the ABBA.
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Post #15,307
10/26/01 4:37:12 PM
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Killed with 00 shot.
-----
Steve
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Post #15,311
10/26/01 4:58:06 PM
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Natural Numbers.
As Ben said, there are two definitions.
[link|http://whatis.techtarget.com/definition/0,,sid9_gci284008,00.html|Here]:
A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways:
N = {0, 1, 2, 3, ...}
N = (1, 2, 3, 4, ...}
The Number Pope (or is it Cardinal Number?) hasn't ruled which is correct. :-P
Cheers,
Scott.
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Post #15,321
10/26/01 6:09:37 PM
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'Has intercourse only with numbers of the opposite class.'
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Post #15,346
10/26/01 10:16:09 PM
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The naturals are...
the basic counting numbers that come up naturally all of the time.
That is how they get their name.
The problem is that zero is special. Whether or not it comes up depends strongly on what you are doing.
For instance in logic, everything in math is built out of the empty set, aka 0. Therefore 0 comes up naturally, and what you get first are 0, 1, 2, ... as the numbers of things in sets. So logicians think of 0 as a natural number.
By contrast in combinatorics (the study of how many ways of producing specific kinds of combinations of things) 0 more often than not either doesn't make any sense, or else is a weird exception. So people who work in combinatorics think of 1, 2, 3, 4,... as natural.
In analytics (you can think of this as the high-falutin' cousin of Calculus) there are a lot of infinite series. These are functions of x written out like this:
a0 * x^0 + a1 * x^1 + a2 * x^2 + ...
As you see, they start with the 0'th term, which is your constant. So any analyst thinks of the natural numbers as 0, 1, 2, 3,...
But if you are a number theorist (ie the kind of person who thinks about things like factoring, primes, etc) then your life is devoted to working with positive integers. So to you the natural numbers look like 1, 2, 3, 4,...
And so it goes. In every area of math you use numbers differently. So whether or not 0 seems like a natural number that keeps on turning up will depend on what you are doing. And really, it doesn't matter. The highschool text books that lecture away on what whole numbers are, versus what natural numbers are, are just BS. The textbook writers needed a distinction, they invented one, and no mathematician really gives a damn.
The fact is that if you can't look beyond terminology to the actual ideas, then math isn't going to be your bag. There are other places where you can throw around lots of terminology without worrying about whether it matters and without trying to figure out what you are talking about. Deconstructionist philosophy for instance. But if you miss the idea for the terminology, mathematicians are likely to notice and wonder WTF you are thinking...
Cheers,
Ben
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Post #15,356
10/26/01 11:57:52 PM
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so to review
if I count, the first whole number is 1 so 1,2,3 is acceptable. If am doing placeholding 0 is the starting point 0,1,2,3 this does matter when designing according to bellcore standards. Went 2 weeks discovering the SS7 congestion messages were being kicked 1,2,3 on one end and 0,1,2 on the other, it took a while for the A-links to sync.
thanx,
bill
tshirt front "born to die before I get old"
thshirt back "fscked another one didnja?"
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Post #15,434
10/27/01 4:17:48 PM
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Exactly
What is natural in one context is different in another.
And it isn't a problem so long as everyone is on the same wavelength. (But that is a big if.)
Cheers,
Ben
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