ozkan12 said:İn a finite set, can we take limit to $\infty$ ?
Also, can you give an example related to infinite subset of $\Bbb{N}$ ?
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
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.
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.
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.
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.
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.