Positive integers, (whole numbers) starting at 1
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The st of counting numbers are called natural numbers. This is taught in math.
The set of counting numbers is a proper subset of the whole number. The latter includes negative counting numbers. Also, there is no consensus as to whether 0 belongs to counting numbers or whole numbers.
The set of Natural Numbers is the set of 'counting numbers' {1,2,3,4,....}. All of them are also real numbers.
The immediate [next] superset is, trivially, the set of natural numbers which consists of the counting numbers and zero. The next significant superset is the set of integers: the counting numbers, their additive inverses (or negatives) and zero.
By definition, the set of counting numbers starts at one and proceeds in ascending order. The next number is 2. If two were not the next number in the set, it would not be the set of counting numbers.