1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

More Limit pts sets

  1. Oct 15, 2008 #1
    Could somebody check this to see if I am right?

    a.) Construct a subset of [tex]\mathbb{R}[/tex] with exactly two limit points.

    [tex]\{ (-1)^n + \frac{1}{n} : n \in \mathbb{N} \} [/tex]

    b.) Find an infinite subset of [tex]\mathbb{R}[/tex] with no limit points.


    c.) Construct a countable subset of [tex]\mathbb{R}[/tex] with countably many limit points.

    [tex]\{1- \frac{(-1)^n}{n}:n \in \mathbb{N} \}[/tex]

    d.) Find a countable subset of [tex]\mathbb{R}[/tex] with uncountably many limit points.

  2. jcsd
  3. Oct 15, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Right. Right. Right. Right. You are getting good at this. Unless in c) you need countably infinity and not just finite.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - More Limit sets Date
Limits of more than one function Oct 8, 2012
One more try at epsilon-delta limits Jul 9, 2012
Two more limit problems Jul 8, 2012
More limits Sep 25, 2010
More limits, just a simple question this time May 19, 2010