# Homework Help: Countable subet

1. Apr 3, 2008

### Doom of Doom

So, the task is to prove: Every infinite set has a infinite countable subset.

2. A set $$S$$ is countable if there exists a bijection $$\phi: \mathbb{N}\rightarrow X$$

3. The attempt at a solution

2. Apr 3, 2008

### Pere Callahan

You can easily construct a countable subset $\{s_1,s_2,\dots\}$ wiht $s_1,s_2,\dots$ being elements of S.

Let $s_1$ be some element of S. Let inductively $s_n$ be some element of $S-\{s_1,\dots,s_{n-1}\}$.

Can you show that this works for any infinte set, and that it does not work for any finite set?

Last edited: Apr 3, 2008