Aleph is Infinite Cardinal

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Theorem

Let $x$ be an ordinal.


Then $\aleph_x$ is an infinite cardinal where $\aleph$ denotes the aleph mapping.


Proof

By the definition of the aleph mapping:

$\aleph : \operatorname{On} \to \mathcal N'$


The theorem statement is an immediate consequence of this fact.

$\blacksquare$