just wanted to point out: isn't a sequence a function defined as

which means a sequence in the set

? So the codomain doesn't have to be

but can be an arbitrary set

? Actually

and

are equivalent right? And a sequence is null when

when

. Also, I like to think of functions as follows: pretend you have a box subdivided into smaller boxes. These smaller boxes represent the elements of the codomain, and the points in the boxes represent the elements of the domain. So a function orders the points in the smaller boxes.