1. The problem statement, all variables and given/known data Suppose V=<Z> where Z is an infinte set, So Z spans V. Suppose that every pair of distinct elements of Z is linearly independent. Is it possible that V is finite dimensional? Justify your answer. 2. Relevant equations 3. The attempt at a solution All the vectors must be linearly independent if any two are so... I dont think you can as a basis for the space would have infinte linaerly independent vectors.