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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


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    Right. Right. Right. Right. You are getting good at this. Unless in c) you need countably infinity and not just finite.
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