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

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Discussion Overview

The discussion revolves around the concept of taking limits to infinity within finite sets, specifically in the context of natural numbers. Participants also explore examples of infinite subsets of the natural numbers.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether limits can be taken to infinity in finite sets, indicating a lack of clarity in the question.
  • Another participant suggests that the set of even integers, represented as $2\mathbb{N}$, serves as an example of an infinite subset of natural numbers.
  • Further contributions mention odd numbers as another example of an infinite subset, alongside the set of prime numbers.
  • It is noted that any sequence $\{a_i\}^{\infty}_1$ where $a_i \in \mathbb{N}$ can be considered an infinite subset of natural numbers.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the first question regarding limits in finite sets, and multiple viewpoints regarding examples of infinite subsets of natural numbers are presented.

Contextual Notes

The discussion lacks clarity on the assumptions underlying the first question about limits in finite sets, and the definitions of "taking limits" are not explicitly stated.

ozkan12
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İn a finite set, can we take limit to $\infty$ ?

Also, can you give an example related to infinite subset of $\Bbb{N}$ ?
 
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ozkan12 said:
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.
 
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
 
ozkan12 said:
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.
 

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