The set of positive integers, of course!
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Traditionally, the set of integers that represents the natural numbers is {1,2,3,...}, which are the positive integers. Some people include the non-negative integers as the set of natural numbers, which is {0,1,2,3,...}, and includes 0.
.{..., -3, -2, -1, 0, 1, 2, 3, ...}
The set of integers includes negative integers as well as positive integers. It also includes the number zero which is neither negative nor positive.
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
The answer below is incomplete.The set of whole numbers also includes all negative integers.