# [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
*>*
*