I just updated the site to be hosted on the root of my site. The URL for the blog still happens to be http://betzster.no-ip.org/blog/, only becuase I also made the homepage the homepage. By this I mean I used the static front page option in WordPress to make http://betzster.no-ip.org point to the homepage and http://betzster.no-ip.org/about-me/ to point to the about page, instead of http://betzster.no-ip.org/blog/home/ or http://betzster.no-ip.org/blog/about-me/.

The permalink structure has been updated to show this, but it looks like there is a permanent redirect that will point all old permalinks to the new one. Very Cool.