# [plt-scheme] Natural numbers

On Wed, Mar 11, 2009 at 10:25:33PM -0400, Stephen Bloch wrote:
>*
*>* 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....
*
That would make sense if half of them grew up on old one's complement
machines, which has a separate plus zero and minus zero in their binary
representations. But that would probably have to be the over-fifty
crowd. Do you teach senior citicens?
-- hendrik