Homework Help: Span of an infinite set. Exam Question.

1. Dec 31, 2008

heshbon

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.

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.

2. Dec 31, 2008

Dick

All of the vectors don't have to be linearly independent just because every pair is. Let Z be the set of all unit vectors in the first quadrant in the two dimensional plane. Since they all point in different directions, any pair is linearly independent.