Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

    [tex]\mathbb{N}[/tex]

    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.

    [tex]\mathbb{Q}[/tex]
     
  2. jcsd
  3. Oct 15, 2008 #2

    Dick

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook