MHB Can we take limits to infinity in finite sets of $\Bbb{N}$?

[ozkan12]

İn a finite set, can we take limit to $\infty$ ?

Also, can you give an example related to infinite subset of $\Bbb{N}$ ?

 

[alyafey22]

İn a finite set, can we take limit to $\infty$ ?

Also, can you give an example related to infinite subset of $\Bbb{N}$ ?

The first question is not clear. For the second one, $2 \Bbb{N}$ which constitutes even integers is a an infinite subset.

 

[ozkan12]

Dear ZaidAlyafey,

Thank you for your attention...For second question odd numbers can be an example...İs there any examples anything else 2N and 2N+1

 

[alyafey22]

Dear ZaidAlyafey,

Thank you for your attention...For second question odd numbers can be an example...İs there any examples anything else 2N and 2N+1

Yes. For example, the set of prime numbers is infinite. More generally, any sequence $\{a_i\}^{\infty}_1$ where $a_i \in \mathbb{N}$ is an infinite subset of natural numbers.