[plt-scheme] Natural numbers

From: Jos Koot (jos.koot at telefonica.net)
Date: Wed Mar 11 23:06:12 EDT 2009

----- Original Message ----- 
From: "Stephen Bloch" <sbloch at adelphi.edu>
To: "Norman Gray" <norman at astro.gla.ac.uk>
Cc: "PLT Scheme ML" <plt-scheme at list.cs.brown.edu>
Sent: Thursday, March 12, 2009 3:25 AM
Subject: Re: [plt-scheme] Natural numbers

> On Mar 11, 2009, at 8:33 PM, Norman Gray wrote:
>> In maths, the term "the natural numbers" refers specifically to the  set 
>> of positive integers (see for example [1]), and not to any set 
>> isomorphic to that.  Thus it does not depend on what you or I may  or may 
>> not find natural, and its meaning is not really a matter for  dispute. 
>> Anyone who refers, in any sort of semi-formal context, to  "the natural 
>> numbers" as meaning anything other than {n in Z : n >  0} is being 
>> quixotic.
> I was brought up with "the natural numbers" meaning {n in Z : n >=  0}. 
> In both my dissertation and my advisor's, and many of the

Usually the letter 'Z;' is used for the set of complex numbers (Q for 
rational numbers and N for natural numbers). If n is a complex number, then 
what is the meaning of 'n>=0'?
You confuse me.

> published papers in my field, it is quite important that the natural 
> numbers include zero.  In fact, I think it's been years if not  decades 
> since I saw "the natural numbers" used formally in a sense  that excluded 
> zero.
>> I don't believe computer scientists have a get-out-of-jail-free  card 
>> here.
> Ah, maybe that's it: I went through graduate school surrounded by 
> logicians and computer scientists. :-)
> Then again, if you ask my programming students, you'll get about a  50/50 
> split on the question of whether zero is positive....
> Stephen Bloch
> sbloch at adelphi.edu
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