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Don't try to "win" the breakup.
Avoid flaunting the fact that you're with other guy directly after the two of you break up. It's okay to go out and enjoy being single, but don't post a million pictures of you with other guys to Facebook, and be sensitive if you know he's going to be there. Don't go on a date with someone to a place where you know you're going to run into him. Try to talk to him, see if you could still be friends so that it isn't making your life awkward. Don't get sucked in if he tries to do this to you, either. Realize that it's his way of trying to prove to you and himself he doesn't care, and take a deep breath and turn the other cheek. If this happens, let him "win" by not retaliating.