5.3 Axioms (optional)
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An axiom is a statement which says something which does not need to be proved. Or rather, something which we decide does not need to be proved. Something which we will assume to be true. We will then try to derive everything else from our axioms.
Example: Peano's axioms
Axioms are most useful in mathematics where we are dealing with abstractions. For example, the following five axioms (Peano's axioms) define the members of the set of natural numbers. Therefore, the type NaturalNumber can be defined by the following five axioms:
Everything that does not satisfy these five axioms is not a natural number. Conversely, everything that satisfies these five axioms is a natural number. Thus these five axioms define the type NaturalNumber by axioms.
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