Real Numbers, From The Ground Up

Natural Numbers: Counting Starting at the most concrete level, a number is a count of how many objects there are. There are six bananas in my fruit basket. I have two children. There are eleven players in a cricket team. And so on. This notion of a number as a count is, for most of us, our first encounter with numbers. Such numbers are vividly reflected in the physical world. They are apparent even to some animals (NYT article).