Is 00 a natural number?

Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number?

It seems as though formerly 0 was considered in the set of natural numbers, but now it seems more common to see definitions saying that the natural numbers are precisely the positive integers.


Simple answer: sometimes yes, sometimes no, it’s usually stated (or implied by notation). From the Wikipedia article:

In mathematics, there are two
conventions for the set of natural
numbers: it is either the set of
positive integers {1,2,3,}
according to the traditional
definition; or the set of non-negative
integers {0,1,2,} according to a
definition first appearing in the
nineteenth century.

Saying that, more often than not I’ve seen the natural numbers only representing the ‘counting numbers’ (i.e. excluding zero). This was the traditional historical definition, and makes more sense to me. Zero is in many ways the ‘odd one out’ – indeed, historically it was not discovered (described?) until some time after the natural numbers.

Source : Link , Question Author : bryn , Answer Author : Noldorin

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