# [plt-scheme] Natural numbers

 From: Jos Koot (jos.koot at telefonica.net) Date: Wed Mar 11 23:06:12 EDT 2009 Previous message: [plt-scheme] Natural numbers Next message: [plt-scheme] Natural numbers Messages sorted by: [date] [thread] [subject] [author]

```----- 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.
Jos

> 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