an ordered pair?
ordered pair (a,b) can be defined in terms of set concepts only. the easiest way to do this is the construction
like you, i'm too lazy to show how this construction works, but it can be shown that (a,b) = (c,d) implies a = c and b = d, and the other way around, so there is a bijection between the set construction and the ordered pair notation
the cartesian product of set A and B is the set of all possible ordered pairs where the first element is from A and the second element is from B
you can apply induction to extend an ordered pair to an n-tuple in a straight forward way (e.g. (a, b, c) = (a, (b, c)) = {{a}, {a, {{b}, {b, c}}}}, etc.)
