Natural Numbers as Cardinals

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Theorem

The natural numbers $\N = \set {0, 1, 2, 3, \ldots}$ can be defined as the set of cardinals.

Proof

From Finite Cardinals form Infinite Set we have that the cardinals form a set which is infinite.

This theorem requires a proof. In particular: Show that the set of finite cardinals satisfy Peano's axioms. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 8$