Finite subsets of the naturals still behave like naturals.
Not precisely. In many ways, yes, but for example they don’t model the axiom of PA that says that every number has a successor.
True, but the axiom of induction holds, and that is the most useful one.
Finite subsets of the naturals still behave like naturals.
Not precisely. In many ways, yes, but for example they don’t model the axiom of PA that says that every number has a successor.
True, but the axiom of induction holds, and that is the most useful one.