Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
2  
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
add comment

1 Answer

up vote 4 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.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.