Exploring Limits and Infinite Subsets of $\Bbb{N}$

In summary, there is no limit to infinity in a finite set and an example of an infinite subset of natural numbers is the set of prime numbers or any sequence where the elements are natural numbers.
  • #1
ozkan12
149
0
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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  • #2
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.
 
  • #3
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
 
  • #4
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.
 

1. What is the concept of "limit" in mathematics?

The concept of limit in mathematics refers to the value that a function or sequence approaches as its input or index approaches a particular value. It is used to describe the behavior of a function or sequence near a certain point or in the infinite limit.

2. How is the concept of limit applied in exploring infinite subsets of $\Bbb{N}$?

In exploring infinite subsets of $\Bbb{N}$, the concept of limit is used to describe the behavior of these subsets as their elements approach infinity. It helps to understand the properties and characteristics of these subsets, such as their size, density, and patterns.

3. What is the significance of studying infinite subsets of $\Bbb{N}$?

Studying infinite subsets of $\Bbb{N}$ is important in understanding the concept of infinity and its applications in mathematics. It also helps in exploring the properties of infinite sets and their relationship with finite sets.

4. How do mathematicians define infinite subsets of $\Bbb{N}$?

Mathematicians define infinite subsets of $\Bbb{N}$ as sets that have an uncountable number of elements. This means that the elements in the subset cannot be listed or counted in a finite amount of time, as they continue indefinitely.

5. What are some common examples of infinite subsets of $\Bbb{N}$?

Some common examples of infinite subsets of $\Bbb{N}$ include the set of all even numbers, the set of all prime numbers, and the set of all powers of a particular number. These subsets have infinitely many elements and exhibit interesting patterns and properties.

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