Accumulation Points: Set with Two or Countably Infinite?

[nitro]

Homework Statement

is there are a set with countably infinite number of accumulation points?

Homework Equations

is there a set with exactly two distinct accumulation points?

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

 

[Unco]

Homework Statement

is there are a set with countably infinite number of accumulation points?

Homework Equations

is there a set with exactly two distinct accumulation points?

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

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, $$\lim_{m\to\infty} y_n+x_m=y_n.$$

 

[nitro]

aahaaaaaaa! :)
thx a lot, i got it