Natural Number is Ordinal/Proof 2

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Theorem

Let $n \in \N$ be a natural number.

Then $n$ is an ordinal.


Proof

From the von Neumann construction of the natural numbers, $\N$ is identified with the minimally inductive set $\omega$.

From Superinductive Class under Successor Mapping contains All Ordinals, it follows by the Principle of Mathematical Induction that every natural number is an ordinal.

$\blacksquare$


Sources