# Vector Space question

by amolv06
Tags: space, vector
 P: 47 1. The problem statement, all variables and given/known data Let R denote the set of real numbers. Define scalar multiplication by $$\alpha x = \alpha x$$ which is simply regular scalar multiplication, and vector addition is defined as $$x \oplus y = max(x,y)$$. 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?
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,904 Yes, that's true. So what is your answer to the question?
 P: 47 Then it is not a proper vector space! Thanks a lot.

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