# [plt-scheme] Natural numbers

----- 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
*>* sbloch at adelphi.edu
*>*
*>*
*>*
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