[plt-scheme] Natural numbers

I guess the tension between logicians and "real" mathematicians shows  
up again. Go look at Quine and his Logic book. -- Matthias (who  
doesn't believe that "real" mathematicians know much about this  
issue :-)



On Mar 11, 2009, at 8:33 PM, Norman Gray wrote:

>
> Greetings.
>
> On 2009 Mar 11, at 23:47, Matthias Felleisen wrote:
>
>> Natural numbers are the counting numbers. You count how many  
>> things you have. (The philosophical way to understand "five" is to  
>> say that it is what all collection of five objects have in common.)
>>
>> The natural (sorry) place to start counting is with 0, having  
>> nothing.
>
> 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 don't believe computer scientists have a get-out-of-jail-free  
> card here.
>
> Best wishes,
>
> Norman
>
>
> [1] http://eom.springer.de/N/n066090.htm
>
> -- 
> Norman Gray  :  http://nxg.me.uk
> Dept Physics and Astronomy, University of Leicester
>