1. The problem statement, all variables and given/known data Let S be a nonempty set and K a field. Let C(S,K) denote the set of all functions [itex]f \in C(S,K) [/itex] such that [itex]f(s) = 0 [/itex] for all but a finite number of elements of S. Prove that C(S,K) is a vector space. OK, I can't make the slightest sense of this. What in the name of all that is holy does the value of f(0) have to do with C(S,K) being a vector space? Can anyone at least hep me figure out what the heck I am supposed to even start with?