Natural number Glossary
Definition
The natural numbers are those used for simple counting: 0, 1, 2, 3, ...
Slightly more technically, they can be seen as the smallest set containing zero and closed under the operation of successor.
.Comments
Some effects of counting with natural numbers can be formulated within first order logic with identity, as this permits the expression of numerical quantifiers.
In Logic for Fun, the natural numbers (or at any rate, the first few of them) constitute a built-in sort. This is because they are extremely useful for expressing many problems that lie on the edge of what can be done just with pure logic. Logic for Fun, in fact, doesn't know about any numbers except for natural ones.
Since any expression built up from a finite alphabet can be given an ID number, which is a natural number, any transformation of input into output, in any language, can be represented as a function from natural numbers to natural numbers. It is for this reason that in computer science we frequently study computability in terms of functions on the naturals.
Some authors do not consider zero to be a natural number, but here we follow Logic for Fun in including it, since it is so useful in practice.