Anorexia doesn't involve vomiting (purging)..that would be bulimia. My doctors have told me that anything involving "purging" calories excessively (ie/ vomiting, excersing all the time, constant movement, etc) is a form of bulimia. Anorexia stems from a latin word meaning "without appetite"- basically anorexics starve themselves. They eat close to nothing or nothing at all, and have trouble eating more. They have an intense fear of gaining weight (which many times can be illogical, ie/ i dont want to get fat so i wont eat the crusts of my bread, or if i eat above 800 calories per day I'll gain weight) Many have a distorted body image (they claim they are fat when in reality they are underweight). A main one is that they stop menstruating, but this is harder to pinpoint if you're worried about a friend or someone you dont really want to ask. If they have stopped though, then it is definately a sign of being underweight. Anorexics also tend to start cooking and reading cook books, even if they never have before (but they never eat the food they make).
