Vector Space question

  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. HallsofIvy

    HallsofIvy 40,382
    Staff Emeritus
    Science Advisor

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

    Thanks a lot.
     
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