Hey I think that school was on an MTV true life ???
But thanks for confirming its existence. What an interesting and vexing debate topic (I used to be a debater). I would have loved to lean something like that, so unless you were rubbing it in her face or something I don't think you did anything wrong. The whole thing just sounds very cute.
BTW I'm in relationship with another super nerd, we correct each other all the time, and have intellectual arguments on the regular, its part of the fun, and the flirting. Next time just ask her out for a coffee, and then you can talk even more about all the cool stuff you know.