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I'm trying to install Firefox. Everytime I download it I can run it but when I take it off my desktop it can no longer be run. What am I not doing correctly?

you need to drag the firefox icon onto you hard drive, preferably into your applications folder.

Yeah, i reckon you're running it from the disk image (.dmg)

You downloaded the file. You ran it. After deleting it, how do you expect it to run?

You probably got that white little box with a firefox logo on it lying on your Desktop. That's a DMG Disk Image. It's like a suitcase carrying stuff. You probably dragged the Icon of Firefox from it to your Desktop. Instead, drag it to your Applications folder in the finder.

Also see: http://www.kamu.ch/switch/index.php?page=art&artid=4

the problem is that you never installed it, and you did what yogi stated, downloaded it, ran it, and then deleted it.

as suggested, drag the file out of the disk image and drop it in your applications folder. you just learned how to install the majority of programs for os x
-chris