>>Define "vector". You can't really, since you haven't properly defined >>a vector space. Hint: axioms.
>I don't understand. A vector is any collection: (x1, ...., x^n) of anything. >In math, the vectors are numbers.
This is wrong. A function can be a vector (usefully so, in fact). A polynomial can be a vector, a sequence can be a vector. In fact, *anything* can be a vector. All that it means to be a vector is to be an element of a vector space (usually the specific vecvtor space is understood from context).