A modern algebra professor took us (his class) on a little two or three week detour of Georg Cantor and infinity. Wow, what a beautiful, eye opening experience that was!
I hate the way elementary math is taught: hit the little brats over the head with a bazillion addition and subtraction problems in the second grade. Similarly with multilplication and division problems in the third grade. Then each year until... oh, I don’t know... the boys are shaving... make them do the same problems over and over again with ever larger numbers. Boooooooooring! By the time they begin algebra, you’re guaranteed they’ll all hate math.
Everyone should be familiar with aleph 0 and aleph 1 by seventh grade!
Yes, and then they are almost prepared for the Snake Lemma http://www.youtube.com/watch?v=etbcKWEKnvg