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I am feeling pretty down that my first number close was a fake number. Now I am starting to question whether I am even a desirable person, because if my first number close was a fake, how many more will be?
Also get used to the fact that you will have to face this feeling quite often in the beginning, and then even after you have a lot of good times, you'll have to face it again when something else weird happens or you screw something up.
This is when you can further your progress the most, by facing this and finding the drive to overcome it.
From the moment you take the FIRST single course of action, you always have something to look back on and say - look what I did that I wouldn't have done before. If I stopped before then, I wouldn't have done it. So why should I stop now.
Heh, notice I left off the ? - cause it's a rhetorical statement, not a question.
For you, the thing you can look back on is actually approaching the girl, and having a course of interaction with her. Even if it went badly, you have something to learn from.
If you didn't do anything you wouldn't learn anything.