The purchased apps section will show all the apps you've ever bought/downloaded. If you want to delete an app, press it's icon on your screen until it jiggles, and then press the 'x'. Mind you, it'll still show up in your 'purchased apps' list. As far as I know, the only way to permanently delete apps is to delete your Apple ID and get a new one, and I'm presuming you don't want to do that.
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