- #1
Dustinsfl
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All numbers of the form $1/n$, $(n = 1,2,3,\ldots)$.$1/n = (0,1)$
The accumulation points are $x\in [0,1]$.
This set is open.
The accumulation points are $x\in [0,1]$.
This set is open.
dwsmith said:All numbers of the form $1/n$, $(n = 1,2,3,\ldots)$.$1/n = (0,1)$
The accumulation points are $x\in [0,1]$.
This set is open.
dwsmith said:All numbers of the form $1/n$, $(n = 1,2,3,\ldots)$.$1/n = (0,1)$
The accumulation points are $x\in [0,1]$.
This set is open.
Sudharaka said:Hi dwsmith, :)
So the set under consideration is, \(S=\{\frac{1}{n}:n\in\mathbb{Z}^+\}\). The definition of a limit point (accumulation point) taking the set of real numbers as the reference space is given >>here<<. If you go by that definition you can prove that the only accumulation point of \(S\) is zero.
Kind Regards,
Sudharaka.
dwsmith said:As with the complex example, why aren't the points of $1/n$ accumulation points as well?
To explore the accumulation points of $1/n$ means to investigate and analyze the values that $1/n$ approaches as $n$ gets closer and closer to infinity.
The accumulation points of $1/n$ can be determined by finding the limit of $1/n$ as $n$ approaches infinity. This can be done by using various mathematical techniques such as L'Hopital's rule or Taylor series.
Exploring the accumulation points of $1/n$ can provide insights into the behavior of the function as $n$ gets larger and larger. It can also help in understanding the concept of infinity and how it relates to mathematical functions.
Yes, the concept of accumulation points is used in many fields such as computer science, physics, and economics. For example, in computer science, understanding accumulation points is crucial in developing efficient algorithms and data structures.
Yes, the concept of accumulation points is closely related to the concepts of limits, sequences, and series. Understanding accumulation points can also help in understanding other topics such as continuity, convergence, and compactness.