Natural Numbers
posted by Tim .
Is this correct, or where did I go wrong in my answer.
Give a reason to support: The natural numbers {1,2,3,4,5,...}are not a group under addition.
My reason:
0 is not included in the group since it is not included by identity property it can not be conducted making this group of numbers not a group under addition.

http://en.wikipedia.org/wiki/Natural_number
set theorists disagree with you. 
Aren't natural numbers also known as counting numbers?