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Is the cardinality of the natural numbers a natural number?

$|\mathbb{N}| \in \mathbb{N}\text{ or } |\mathbb{N}| \notin \mathbb{N}$, that is the question.

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Each natural number is a specific positive integer, so no. Even interpreting $n$ as a set with $n$ elements, it is not equipotent to $N$, an infinite set. – coffeemath Nov 12 '12 at 15:09
up vote 6 down vote accepted

$|\mathbb{N}| \notin \mathbb{N}$

$\mathbb{N}$ doesn't contain any kind of $\infty$. Yes, $\mathbb{N}$ contains huge numbers, but not infinity.

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