First week is pretty well meaningless: your body is adjusting, shedding water, etc. In fact, don't be surprised if you don't lose any weight at all next week: if that happens, it's just that you DID burn fat but you also regained some water.
I lost big numbers the first couple weeks then things slowed down to a pound or two a week. I agree that some of it is water weight. That is why fad diets like the soup diet appear to work. The dieter changes their habits just long enough to lose the water weight and think they are seeing fat burning results. Fat, water or a combination of both are still reasons to celebrate your loss and your great start
Failure is only a fact when you give up. Everyone gets knocked down, the question is: Will you get back up?