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Accumulation points!

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data
    is there are a set with countably infinite number of accumulation points?

    2. Relevant equations

    is there a set with exactly two distinct accumulation points?

    3. The attempt at a solution
    a set with two accumulation points might be: {1/n + (-1)^n}
    i have no clue about the countably infinite one

    hope someone could help!

    thx a lot
  2. jcsd
  3. Feb 7, 2009 #2
    Your idea is fine, but be sure to write it correctly (with an ": n in N").

    I'd prefer not to spoon feed you an example for the other; rather, consider perhaps a set (in R) that depends on two natural numbers. Say, [tex]\{y_n, y_n + x_m: n, m \in \mathbb{N}\}[/tex], which you might construct so that [tex]\lim_{m\to\infty} x_m = 0[/tex] and so, for each fixed n, [tex]\lim_{m\to\infty} y_n+x_m=y_n.[/tex]
    Last edited: Feb 7, 2009
  4. Feb 7, 2009 #3
    aahaaaaaaa!! :)
    thx a lot, i got it
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