1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Span of an infinite set. Exam Question.

  1. Dec 31, 2008 #1
    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.
  2. jcsd
  3. Dec 31, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Span of an infinite set. Exam Question.
  1. Spanning set (Replies: 8)