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## The Naturals, Axiomatically Speaking

We’ll start by talking about the basic fundamental group of numbers: the naturals. The natural numbers (written N) consist of zero and the numbers greater than zero that can be written without fractions.

When you talk about numbers, you start with the natural numbers because they’re the most basic fundamental sort of number. Intuitively, natural numbers are the first mathematical concepts that we understand as children. They’re the whole numbers, with no fractions, starting at zero and going onward toward infinity: 0, 1, 2, 3, 4, …. (Computer scientists like me are particularly fond of natural numbers because everything computable ultimately comes from the natural numbers.)

The natural numbers are actually ...

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