# [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
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