Social Awkwardness

You know how you often get introduced to the same person multiple times? As we all know this is because people tend to forget the names of other people. Now when I get in one of these situations, I am always happy to re-introduce myself and learn the other person's name again if necessary. My problem is that I can never bring myself to say, "Nice to meet you." There's just something wrong about it because it is not true. I have met the person before. So I might say, "Nice to see you again," but I almost never say, "Nice to meet you" to someone I have met before. More often than not, I just mumble something and seem even less polite.