Bradd W. Szonye wrote:
>> I suspect that you have natural numbers and whole numbers confused.
>> The natural numbers are the non-negative integers, and the whole
>> numbers are the positive integers.  [...]  "Non-negative integer" and
>> "natural number" are synonymous.

Category 5 wrote:
> Your usage of 'whole number' is correct, though the term is used
> infrequently in mathematics.  The natural numbers, on the other hand,
> may just as easily exclude zero as include it - there is no complete
> consensus here, mainly because different branches find one or the
> other definition most convenient.

Odd, I've always seen the two sets defined thus (naturals include 0,
wholes don't), from grade-school through university math.

> This article may be helpful:
>
> http://wikipedia.org/wiki/Natural_number

Note:

    In the nineteenth century, a set-theoretical definition of natural
    numbers was developed. With this definition, it was more convenient
    to include zero (corresponding to the empty set) as a natural
    number. Wikipedia follows this convention, as do set theorists,
    logicians, and computer scientists. Other mathematicians, primarily
    number theorists, often prefer to follow the older tradition and
    exclude zero from the natural numbers.

Computer scientists include 0 because it's the first Peano-Church
number. Anyway, this explains why it's the only definition I've seen:
Both the grade-school and university computer science curricula taught
natural numbers in the context of set theory.
--
Bradd W. Szonye
http://www.szonye.com/bradd