[plt-scheme] Natural numbers

From: Stephen Bloch (sbloch at adelphi.edu)
Date: Wed Mar 11 22:25:33 EDT 2009

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  
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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