I am having a fair amount of trouble with what would appear to be a very straight forward question. The question states:

Show that the set consists of all real sequences converging to zero is a vector space and show that it is not finite dimensional.

If anyone could give me a rough idea how to get started on this question or how to approach it, I would be very appreciative. Thanks.

Edit: I should also point out that the english is very bad lol, it should probably read something like: Show that the set "which" consists ....