What is a Natural numbers?

Natural Numbers

Natural numbers are the simple counting numbers (0, 1, 2, 3, 4, . . .). The skill of counting is intimately linked to the development of complex societies through trade, technology, and documentation. Counting requires more than numbers, though. It involves addition, and hence subtraction too.

As soon as counting is introduced, operations on numbers also become part of the lexicon—numbers stop being simple descriptors, and become objects that can transform each other. Once addition is understood, multiplication follows as a way of looking at sums of sums—how many objects are in five groups of six?—while division offers a way of describing the opposite operation to multiplication—if thirty objects are divided into five equal groups, how many objects are in each?

But there are problems. What does it mean to divide 31 into 5 equal groups? What is 1 take away 10? To make sense of these questions we need to go beyond the natural numbers.