Natural numbers

The natural numbers are the basis of all of mathematics. To create a natural number we can write: Another way to write the same thing, which involves less bracket matching is: For convenience we can also just write the number as a decimal and it will convert it to a natural number. We can multply two natural numbers together: Equality:

Internal Representation

For speed and efficiency, the internal representation of natural numbers is not S(S(S(S(...0)))) but uses machine arithmetic. $$\sqrt{1}$$