Is 0 a Natural Number?
Subash, a user of my math site (Interactive Mathematics) asked recently whether 0 is a Natural Number or not. My reply:
Normally I have always taken the Natural Numbers to start at 1 and not to include zero. I used to get my students to remember this by saying the natural numbers can be counted using your fingers and the first finger looks like a 1, while the word “whOle” has a zero in the middle.
Thoughts by others:
According to Dr Math:
Natural Numbers are 1,2,3,4,5,… [...] and Whole numbers are 0,1,2,3,…
According to Wikipedia:
In mathematics, a natural number is either a positive integer (1, 2, 3, 4, …) or a non-negative integer (0, 1, 2, 3, 4, …). The former definition is generally used in number theory, while the latter is preferred in set theory and computer science.
The safest thing is to state whether you are including 0 or not when talking about Natural Numbers. You could write it something like:
“The Natural Numbers (taken as 1,2,3,4,…) are blah blah blah.”
So who cares? This situation is strange because mathematics is normally a very precise science and there is normally broad agreement about such definitions. Anwyay, it matters if students lose marks in assessments because there is disagreement about the definition. So the set theorists and the computer scientists should just conform… 
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vlorbik said,
October 11, 2007 at 9:10 pm
i call the positive integers “the positive integers”
(and use the BlackBoardBold symbol ${\Bbb Z}^+$).
the “natural numbers” are (of course!) N = {0, 1, 2 …}.
and “whole numbers” is just slang for “integers”
(i.e., is left with no formal definition at all).
textbooks have done a pretty good job of muddying
the waters here … but i think these definitions come close
to industry standard (note that there’s no Bbb symbol–
like N, Z, Q, R, C, and even H– called “W”; this is because
this language was created by people who like to feel
smarter than their students [compare "ln" versus "log":
the big kids get to call the natural log by its right name
but *you* little boys and girls aren't ready for that yet...]).
zac said,
October 11, 2007 at 11:09 pm
Thanks for your input, Vlorbik.
I’m with you on the “ln-log” issue, something I have found silly for a long time, especially as many students here in Singapore write it with an ‘eye’ rather than ‘ell’ as in
not
Grrr…
Don’t miss Towards more meaningful math notation where related issues are discussed.
Arvind said,
August 20, 2008 at 6:39 pm
Now that we have accepted 0-9 and 11-19 as counting tables,it is high time to give up various nomenclature and accept ‘0′ as Natural Number and include in set N