1. ## Bounded Sequence

Give an example of bounded sequence that does not converge.

2. The most straightforward one :

$(-1)^n$

3. Non-convergent Cauchy sequences will be bounded as well.

4. Originally Posted by redsoxfan325
Non-convergent Cauchy sequences will be bounded as well.
For this to work you must be working in a non-complete metric space. So this isn't going to happen in $\mathbb{R}^n$

5. Originally Posted by putnam120
For this to work you must be working in a non-complete metric space. So this isn't going to happen in $\mathbb{R}^n$
We aren't in $\mathbb{R}^n$.