The Natural Numbers

Firstly, it should be mentioned that almost all mathematicans denote the integers --- the numbers, ..., -3, -2, -1, 0, 1, 2, 3, ... --- by the symbol Z. But often one like to disgard the negative numbers among these and often the zero is also disliked. So, the question arises: 'What are the natural numbers?'. There is a controverse among mathematicians, whether one should use the symbol N including or excluding the 0. For some purpose like arithmetic it is more convincient to regard zero as a natural number, but for others like number theory one prefers to exclude it. There are some fighters, like J. H. Conway, which even enumerate the chapter of their book starting from 0 to propagate their definition.

It is clear, that a unique notion is worthwhile to avoid misunderstanding. Hence, what are the main reasons for 0 e N, or not in N?
Those people who agree with this definition, like a logic of set definition and identify the 'first' number by the empty set. The next number is always defined recursively, to be the set consisting only of its predecessor. So the number of elements of this sequence of sets is 0, 1, 2, ... And because logic is the basic of mathematics, this must be the true definition of the natural numbers.
These people who incline to call 0 a natural number, argue that 0 is not a natural counter. Humans always start counting from 1 if we look back into history. So , N should start with 1. Furthermore, an object exists, if and only if there are n e N examples of it. Or formulated ironically: 'Look, there are 0 tychanitons!' What is more nature-like ?
And there are mathematicains who dislike this psychologic symbol-war and only speek of positive integers or nonnegative integers.
And my private oppinion? Well, I use occasionally the symbol N₀. :)