Class of All Cardinals Contains Minimally Inductive Set

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Theorem

Let $\NN$ denote the class of all cardinal numbers.


Then:

$\omega \subseteq \NN$

where $\omega$ denotes the minimally inductive set.


Proof

Suppose $n \in \omega$.

By Cardinal of Finite Ordinal, $n = \card n$.

By Cardinal of Cardinal Equal to Cardinal/Corollary, $n \in \NN$.

$\blacksquare$


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