The i vs. j thing for imaginary numbers is usually an engineering/physics divide. I was told it was because engineers have a silly habit of using i for current and since you use imaginary numbers in decribing current and voltage in circuits, two different uses for the same letter would be confusing.

When I took real analysis (a hardcore math course in which we started by proving 2 > 1 and ended the year eight months later proving how to do calculus) we had natural numbers (N), that is, the "counting numbers" 0, 1, 2, 3,..., integers (...,-3, -2, -1, 0, 1, 2, 3...) (symbolized by Z - why has no one else mentioned Z?), rational numbers (Q) (any number that can be written as the quotient of two integers), irrational numbers (I, I think) (any number that CAN'T be written as the quotient of two integers), real numbers (R) (rational and irrational together), and complex numbers (C) which included all the others.

Note that for all of those the symbol is not just the letter but the funny letter with an extra bar which is completely unreproducible outside of TeX. (Having said that, maybe I'll make a little TeX file and post it somewhere so you can see what I mean. Give me an hour or two...I'm supposed to be working!)

Anyway, the naming is probably not so important as knowing what differentiates one group from another, what properties make one group different from the other.

emanuela could probably give us some definitive definitions on what's current in the "real math" world (rather than the bizarre world of the inconsistent drivel they teach kids in school - all you have to do is change provinces and the natural numbers could take on a whole different meaning - they should get their act together!).