# Bounded Sequence

• September 18th 2009, 08:27 AM
tigergirl
Bounded Sequence
Give an example of bounded sequence that does not converge.
• September 18th 2009, 08:30 AM
Moo
The most straightforward one :

$(-1)^n$
• September 18th 2009, 12:11 PM
redsoxfan325
Non-convergent Cauchy sequences will be bounded as well.
• September 20th 2009, 06:56 AM
putnam120
Quote:

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 $\mathbb{R}^n$
• September 20th 2009, 08:50 AM
redsoxfan325
Quote:

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 $\mathbb{R}^n$.