I think everyone understands the concept of "nothing" or "no cookie" vs "a cookie", just as babies (and, say, birds [1]) have a concept of quantity and even discrete quantity at small values.

I can understand that I have no cookie without counting from the number 0. But why is it important to label nothing, to give it a name and symbol and define its properties?

[1] http://en.wikipedia.org/wiki/Bird_intelligence#Counting