“Any number is an abstraction, a recognition that collections may have something in common even if the elements of the collections are very different. The number 2 is the common property of all sets containing a pair, the number 3 of all sets that contain a triple, and so on. However, although they are abstract and demanding, positive integers correspond to real ‘things’ that can be enumerated. Therefore,we first learn to count small numbers of items and later use this counting procedure to comprehend infinite positive numbers.
Zero, however, does not fit into this routine. While counting is based on the assumption that there is something to be counted, a set with no elements cannot be assessed via counting. Understanding that zero is still a collection (even if empty) and a numerical concept requires abstract thinking that is detached from emprical experiance. The problem is that ‘nothing’ needs to become ‘something’. The absence of elements needs to become a mental category- a mathmatical object.
As a reflection of this mental challenge, it took a long strech of human history for zero to be recognized and appreciated.”
Andreas Nieder, Representing Something Out of Nothing: The Dawning of Zero, Trends in Cognative Science, Vol. 20, No. 11, November 2016