answersLogoWhite

0

If x is a cluster point for the sequence {x_n}, there is a subsequence of {x_n} whose limit is x. The subsequence can be constructed by choosing a sequence of shrinking neighborhoods V_k about x. Since x is a cluster point, each such neighborhood contains infinitely many elements of {x_n}. By choosing a new point x_k from each neighborhood V_k, we get a subsequence {x_k} of {x_n} with lim x_k = x.

User Avatar

Wiki User

12y ago

Still curious? Ask our experts.

Chat with our AI personalities

EzraEzra
Faith is not about having all the answers, but learning to ask the right questions.
Chat with Ezra
RafaRafa
There's no fun in playing it safe. Why not try something a little unhinged?
Chat with Rafa
LaoLao
The path is yours to walk; I am only here to hold up a mirror.
Chat with Lao

Add your answer:

Earn +20 pts
Q: Why limit related with cluster point?
Write your answer...
Submit
Still have questions?
magnify glass
imp