# Accumulation points!

1. Feb 7, 2009

### nitro

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. Feb 7, 2009

### Unco

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, $$\{y_n, y_n + x_m: n, m \in \mathbb{N}\}$$, which you might construct so that $$\lim_{m\to\infty} x_m = 0$$ and so, for each fixed n, $$\lim_{m\to\infty} y_n+x_m=y_n.$$

Last edited: Feb 7, 2009
3. Feb 7, 2009

### nitro

aahaaaaaaa!! :)
thx a lot, i got it

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