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Vector Space question

  1. Feb 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Let R denote the set of real numbers. Define scalar multiplication by [tex]\alpha x = \alpha x[/tex] which is simply regular scalar multiplication, and vector addition is defined as [tex]x \oplus y = max(x,y)[/tex]. Is R a vector space with these operations?

    2. Relevant equations

    Some given above.

    3. The attempt at a solution

    There seems to be no zero vector to this equation as for any number k there exists another number k-1, so there is no single 0 vector for a vector space with the operations defined above. Is this reasoning correct?
  2. jcsd
  3. Feb 25, 2008 #2


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    Staff Emeritus
    Science Advisor

    Yes, that's true. So what is your answer to the question?
  4. Feb 27, 2008 #3
    Then it is not a proper vector space!

    Thanks a lot.
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