The discussion centers on the concept of limits in finite sets, specifically questioning whether limits can be taken to infinity within finite subsets of the natural numbers, denoted as $\Bbb{N}$. It is established that limits cannot be taken to infinity in finite sets. However, examples of infinite subsets of $\Bbb{N}$ are provided, including the set of even integers represented as $2\Bbb{N}$, odd integers as $2\Bbb{N}+1$, and the set of prime numbers. These examples illustrate the nature of infinite sequences within the natural numbers.
PREREQUISITESMathematicians, students of mathematics, and educators seeking to deepen their understanding of set theory, limits, and the properties of natural numbers.
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