Ok, so in discussion today we were talking about combinatonics and counting. We were going over binomial coeffients, and i didn't like the explanation, and i related it to "its like, when you're learning to multiply, and they tell you two negatives equal a positive because when you put one minus sign on top of the other it makes a plus sign." But moving the lines around doesn't actually explain why two negatives equal a positive, its just a conveinient way of learning it so you can do the problems right. ...but then someone asked me after class, "why DO two negatives equal a positive?" and i was like "err... cause multiplication is the addition of groups and when you have a negative and you put it into negative groups... Hmmph! i don't actually know dammit!" So, i've been chewing it over, and i think i've made some sense thinking about it in terms of negative meaning direction, and multiplying meaning you increase the magnitude... but i dunno.... i want a better explanation. Please.